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Introduction to Logic: Exam Study

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Questions and Answers

What is the logical connective that represents 'if and only if'?

$\equiv$ (correct)
$\land$
$\supset$
$\lor$

Which logical operator is used to express negation?

. (dot)
V
~ (correct)
$\supset$

Which of the following represents a conditional statement?

A . B
A $\supset$ B (correct)
A V B
A $\equiv$ B

If P is 'It is raining' and Q is 'I will take an umbrella', which logical expression represents 'It is raining and I will take an umbrella'?

P . Q (C) Signup and view all the answers

What is the interpretation of 'A V B'?

A or B (or both) (D) Signup and view all the answers

If statement 'A' is 'The sun is shining', what does '~A' represent?

The sun is not shining. (C) Signup and view all the answers

Which connective could be accurately described as 'moreover'?

. (D) Signup and view all the answers

If P represents 'I study hard' and Q represents 'I will pass the exam', how would you logically represent the statement 'If I study hard, then I will pass the exam'?

P $\supset$ Q (B) Signup and view all the answers

What is a key difference between '$\supset$' and '$\equiv$'?

$\supset$ only indicates condition, while $\equiv$ indicates equivalence. (A) Signup and view all the answers

How does 'V' differ from '.' in logical statements?

'V' indicates a disjunction, while '.' indicates a conjunction. (C) Signup and view all the answers

Flashcards

~ (tilde)

Indicates negation or the opposite of a statement. It signifies 'not' or 'it is not the case that'.

. (dot)

Indicates conjunction, joining two statements. Means 'and', 'also', or 'moreover'.

V

Represents disjunction, indicating either/both of the statements are the case. Means 'or' or 'unless'.

⇒

Denotes a conditional statement. If the first part is true, then the second part is also true. Means 'if, then, only if'.

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≡

Indicates a biconditional statement. Both statements must be true or false together. Means 'if and only if'.

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Study Notes

~ means "not, it is not the case that"
. means "and, also, moreover"
V means "or, unless"
⊃ means "if, then, only if"
≡ means "if and only if"

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