3: Logical Values

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Questions and Answers

Which logical operator is used for conjunction in C++?

&& (correct)

The logical operator OR in C++ is represented by the symbol '!'

False

What is the result of the boolean expression (1 && 0)?

In a truth table, the negation (logical NOT) of a boolean value x is represented as ____.

¬x Signup and view all the answers

Match the following logical operators with their corresponding symbols in C++:

Logical AND = && Logical OR = || Logical NOT = ! Signup and view all the answers

If x is true and y is false, what is the result of x || y?

true Signup and view all the answers

The logical expression (a % 2 == 0) evaluates to true if a is an odd number.

False Signup and view all the answers

Write the C++ expression for logical NOT of a boolean variable b.

!b Signup and view all the answers

Which of the following functions can be used to represent the function f0000?

x ∧ ¬x Signup and view all the answers

The identity x ∨ y = ¬(¬x ∧ ¬y) implies that conjunction and negation are sufficient to generate all binary logical functions.

True Signup and view all the answers

What values can be converted from int to bool in C++?

Any non-zero integer converts to true, while 0 converts to false. Signup and view all the answers

According to De Morgan's rules, !(a ∧ b) is equivalent to ______.

!a ∨ !b Signup and view all the answers

Match the logical operation with its De Morgan's equivalent:

!(a && b) = !a || !b !(a || b) = !a && !b Signup and view all the answers

What does the conversion of the boolean value 'true' to int result in?

1 Signup and view all the answers

It is a good idea to use int instead of bool in C++ programs.

False Signup and view all the answers

What does the expression f(x, y) ∨ g(x, y) yield true?

It yields true if either f(x, y) or g(x, y) is true. Signup and view all the answers

What is the result of x ⊕ y when both x and y are true (1)?

0 Signup and view all the answers

The expression x ⊕ y is true when both x and y are true.

False Signup and view all the answers

What logical operators can express any binary logical operator according to the theorem?

AND, OR, NOT Signup and view all the answers

The characteristic vector of the XOR operation x ⊕ y is represented as __________.

0110 Signup and view all the answers

Match the following functions to their corresponding characteristic vectors:

x ∧ y = 0001 x ∧ ¬y = 0010 ¬x ∧ y = 0100 ¬x ∧ ¬y = 1000 Signup and view all the answers

In the truth table for (x ∨ y) ∧ ¬(x ∧ y), what is the value when x=0 and y=1?

1 Signup and view all the answers

What is the result of the expression `!(n < 0)` when `n` is equal to 1?

true Signup and view all the answers

The negation operator `!` has a lower precedence than the conjunction operator `&&`.

False Signup and view all the answers

Any characteristic vector can represent a binary logical function with at least one true outcome.

True Signup and view all the answers

What is the meaning of right associative in the context of the negation operator?

The negation operator evaluates from right to left. Signup and view all the answers

Write the expression for XOR using the canonical functions.

(x ∨ y) ∧ ¬(x ∧ y) Signup and view all the answers

In C++, the operator `&&` is known as the __________ operator.

conjunction Signup and view all the answers

Match the following logical operators with their associated meaning:

&& = Logical conjunction || = Logical disjunction ! = Logical negation Signup and view all the answers

Which of the following expressions gives a result of false if `n` is 1 and `p` is 0?

(n < 0) || (0 < p) Signup and view all the answers

What is the result of the expression '(x || y) && !(x && y)'?

True if either x or y is true, but not both Signup and view all the answers

The expression `a && b || c && d` is equivalent to `(a && b) || (c && d)`.

True Signup and view all the answers

What is the result of the expression `7 + x < y && y != 3 * z || !b` if `x` is 2, `y` is 10, `z` is 3, and `b` is false?

true Signup and view all the answers

Short circuit evaluation prevents unnecessary calculations in logical expressions.

True Signup and view all the answers

What will happen if 'x' is 0 in the expression 'bool b = (x != 0) && z / x > y'?

The second expression 'z / x > y' will not be evaluated, preventing division by zero. Signup and view all the answers

The syntax for an if-statement is 'if (condition) _______;'.

statement Signup and view all the answers

Match the logical expressions with their descriptions:

(x || y) && !(x && y) = x or y, and not both !(!x && !y) = not none (x || y) && (!x || !y) = x or y, and one of them not !(!x && !y || x && y) = not: both or none Signup and view all the answers

What is the role of the 'if-else' statement?

To select one of two possible branches based on a condition Signup and view all the answers

The expression 'if (a % 2 == 0)' checks if 'a' is odd.

False Signup and view all the answers

In a selection statement, what determines whether the body of the statement executes?

The truth value of the condition. Signup and view all the answers

Study Notes

Introduction to Computer Science Course Information

Course name: Introduction to Computer Science
Course IDs: 252-0032, 252-0047, 252-0058
Authors: Manuela Fischer and Felix Friedrich
Department: Computer Science, ETH Zurich
Semester: Fall 2024

Logical Values

Goal: To understand conditional code execution
Boolean expression: A condition used for conditional execution
Code Example 4.1: Demonstrates conditional execution based on integer input ('a'). If 'a' is even, it prints "even"; otherwise, it prints "odd".
Boolean Values are represented as 0 (false) or 1 (true) in mathematics.
C++ uses the bool type for logical values, with literals false and true.
Relational operators: Used for comparisons between values of arithmetic types
- < (less than)
- <= (less than or equal to)
- > (greater than)
- >= (greater than or equal to)
- == (equal to)
- != (not equal to)
Logical Operators offered in C++: && (AND), || (OR), !(NOT)

Boolean Functions and Logical Operators

Conjunction (logical AND): True only if both operands are true
Disjunction (logical OR): True if at least one operand is true
Negation (logical NOT): True if the operand is false

Precedences

Evaluation order of boolean expressions is determined by operator precedence and associativity.
Unary negation (!) has higher precedence than binary logical operators (&&, ||).
Binary conjunction (&&) has higher precedence than binary disjunction (||).
The order of operations should be carefully considered when evaluating a Boolean expression

Completeness

C++ offers logical operators AND, OR and NOT
These canonical operators can be used to define any binary boolean function.
XOR (exclusive or): True if exactly one operand is true (e.g., a XOR b = (a OR b) AND NOT (a AND b))

Conversion

bool values can be converted to integers (true = 1, false = 0)
Integer values not equal to 0 can be converted into true values.

The Rules of De Morgan

De Morgan's laws provide rules to negate boolean expressions.

Short-Circuit Evaluation

Optimization technique for evaluating boolean expressions.
Expression evaluation stops if the result is already known from the first operand. (e.g. a && b and if a is false, b will never be evaluated).

Control Statements

If-statements
If-else statements

Iteration Statements

For statements
While statements
Do-while statements

Switch Statements

Alternative to multiple if-else statements for case distinction.

Visibility

Variables are only accessible within their scope.
Inner scopes can shadow variables declared in outer scopes.

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Description

This quiz focuses on logical values and conditional code execution in C++. It covers Boolean expressions, relational operators, and logical operators essential for implementing conditions in programming. Perfect for understanding core programming concepts in your computer science journey.

3: Logical Values

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Questions and Answers

Which logical operator is used for conjunction in C++?

The logical operator OR in C++ is represented by the symbol '!'

What is the result of the boolean expression (1 && 0)?

In a truth table, the negation (logical NOT) of a boolean value x is represented as ____.

Match the following logical operators with their corresponding symbols in C++:

If x is true and y is false, what is the result of x || y?

The logical expression (a % 2 == 0) evaluates to true if a is an odd number.

Write the C++ expression for logical NOT of a boolean variable b.

Which of the following functions can be used to represent the function f0000?

The identity x ∨ y = ¬(¬x ∧ ¬y) implies that conjunction and negation are sufficient to generate all binary logical functions.

What values can be converted from int to bool in C++?

According to De Morgan's rules, !(a ∧ b) is equivalent to ______.

Match the logical operation with its De Morgan's equivalent:

What does the conversion of the boolean value 'true' to int result in?

It is a good idea to use int instead of bool in C++ programs.

What does the expression f(x, y) ∨ g(x, y) yield true?

What is the result of x ⊕ y when both x and y are true (1)?

The expression x ⊕ y is true when both x and y are true.

What logical operators can express any binary logical operator according to the theorem?

The characteristic vector of the XOR operation x ⊕ y is represented as __________.

Match the following functions to their corresponding characteristic vectors:

In the truth table for (x ∨ y) ∧ ¬(x ∧ y), what is the value when x=0 and y=1?

What is the result of the expression !(n < 0) when n is equal to 1?

The negation operator ! has a lower precedence than the conjunction operator &&.

Any characteristic vector can represent a binary logical function with at least one true outcome.

What is the meaning of right associative in the context of the negation operator?

Write the expression for XOR using the canonical functions.

In C++, the operator && is known as the __________ operator.

Match the following logical operators with their associated meaning:

Which of the following expressions gives a result of false if n is 1 and p is 0?

What is the result of the expression '(x || y) && !(x && y)'?

The expression a && b || c && d is equivalent to (a && b) || (c && d).

What is the result of the expression 7 + x < y && y != 3 * z || !b if x is 2, y is 10, z is 3, and b is false?

Short circuit evaluation prevents unnecessary calculations in logical expressions.

What will happen if 'x' is 0 in the expression 'bool b = (x != 0) && z / x > y'?

The syntax for an if-statement is 'if (condition) _______;'.

Match the logical expressions with their descriptions:

What is the role of the 'if-else' statement?

The expression 'if (a % 2 == 0)' checks if 'a' is odd.

In a selection statement, what determines whether the body of the statement executes?

Study Notes

Introduction to Computer Science Course Information

Logical Values

Boolean Functions and Logical Operators

Precedences

Completeness

Conversion

The Rules of De Morgan

Short-Circuit Evaluation

Control Statements

Iteration Statements

Switch Statements

Visibility

Other topics:

Studying That Suits You

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What is the result of the expression `!(n < 0)` when `n` is equal to 1?

The negation operator `!` has a lower precedence than the conjunction operator `&&`.

In C++, the operator `&&` is known as the __________ operator.

Which of the following expressions gives a result of false if `n` is 1 and `p` is 0?

The expression `a && b || c && d` is equivalent to `(a && b) || (c && d)`.

What is the result of the expression `7 + x < y && y != 3 * z || !b` if `x` is 2, `y` is 10, `z` is 3, and `b` is false?