Q1 · easy · AI-verified
If p: 'It is raining' and q: 'The ground is wet', then the compound statement p ∧ q means:
- It is raining or the ground is wet.
- It is not raining and the ground is not wet.
- It is raining and the ground is wet.
- If it is raining, then the ground is wet.
Q2 · medium · AI-verified
How many rows are required in a truth table for a compound statement involving 3 simple statements p, q, and r?
- 6
- 9
- 8
- 4
Q3 · hard · AI-verified
Let p: 'x is an even number' and q: 'x is divisible by 4'. Which of the following is the correct negation of the statement 'If x is an even number, then x is divisible by 4'?
- x is not an even number or x is divisible by 4
- x is an even number and x is not divisible by 4
- If x is not divisible by 4, then x is not an even number
- x is not an even number and x is not divisible by 4
Q4 · hard · AI-verified
If the statement 'p ↔ q' is false, which of the following must be true?
- Both p and q are true
- p and q have different truth values
- Both p and q are false
- p is true and q is true
Q5 · medium · AI-verified
The statement 'p if and only if q' (p ↔ q) is TRUE when:
- Both p and q have the same truth value.
- At least one of p or q is True.
- p is False and q is True.
- p is True and q is False.