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Questions and Answers
Which of the following is a statement?
Which of the following is a statement?
- $y$ is odd
- $x^2 = 10$
- For all real numbers $a$, $a^2 >= 0$ (correct)
- $x + 10$
Which of the following statements has truth value 'T'?
Which of the following statements has truth value 'T'?
- $3$ is a prime number (correct)
- $1$ is an odd number (correct)
- $1$ is a prime number
- None of the above
For all $x$, $P(x)$ is false if
For all $x$, $P(x)$ is false if
- There is a $x$ for which $P(x)$ is true
- $P(x)$ is false for every $x$ (correct)
- $P(x)$ is true for only some $x$
- There is a $x$ for which $P(x)$ is true
The symbol '->' represents
The symbol '->' represents
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Which of the following is a conditional statement?
Which of the following is a conditional statement?
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Which of the following is a conjunction?
Which of the following is a conjunction?
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Study Notes
Statements and Truth Values
- A statement is a sentence that is either true or false, but not both.
- For example, "For all real numbers $a$, $a^2 >= 0$" is a statement because it is always true.
- On the other hand, "$x + 10$" is not a statement because it is an expression that can be true or false depending on the value of $x$.
Truth Values
- The truth value of a statement is either 'T' (true) or 'F' (false).
- For example, the statement "$3$ is a prime number" has a truth value of 'T' because it is true.
- The statement "$1$ is a prime number" has a truth value of 'F' because it is false.
Conditional Statements
- A conditional statement is a statement that can be written in the form "if $p$ then $q$".
- For example, "If $2 = 2$ then $2$ is prime" is a conditional statement.
- The symbol '->' is often used to represent "if and then" in conditional statements.
Conjunctions
- A conjunction is a statement that combines two or more statements using the word "and".
- For example, "$x$ is odd and $15$ is composite" is a conjunction.
- The truth value of a conjunction is 'T' only if all the individual statements are true.
Disjunctions
- A disjunction is a statement that combines two or more statements using the word "or".
- For example, "$3 = 0$ or $2$ is even" is a disjunction.
- The truth value of a disjunction is 'T' if at least one of the individual statements is true.
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