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Question
If (p∧∼q)∧(p∧r)→∼p∨q is false, then the truth values of p,q are r, respectively :
If (p∧∼q)∧(p∧r)→∼p∨q is false, then the truth values of p,q are r, respectively :
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Solution
The correct option is B T,F,T
using truth table
p q r p∧rq p∧r (p∧rq)∧p∧r ∼p∨q (p∧rq)∧p∧r→∼p∨q T T T F T F T T T T F F F F T T T F T T T T F F T F F T F F F T F T T F F F T T F T F F F F T T F F T F F F T T F F F F F F T T
The only possible choice is if p=Tq=Fr=T
using truth table
| p | q | r | p∧rq | p∧r | (p∧rq)∧p∧r | ∼p∨q | (p∧rq)∧p∧r→∼p∨q |
| T | T | T | F | T | F | T | T |
| T | T | F | F | F | F | T | T |
| T | F | T | T | T | T | F | F |
| T | F | F | T | F | F | F | T |
| F | T | T | F | F | F | T | T |
| F | T | F | F | F | F | T | T |
| F | F | T | F | F | F | T | T |
| F | F | F | F | F | F | T | T |
The only possible choice is if
p=T
q=F
r=T
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