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Let p, q and r be three logical statements with truth values F, T and F respectively, then the truth value of (~ p ⇒ ~ q) v r is
- a)T
- b)F, if r had truth value T
- c)F
- d)F, if q had truth value F
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let p, q and r be three logical statements with truth values F, T and ...
Q) ∧ r is F.
To see why, let's break down the expression:
- ~p means "not p", so if p is false (F), then ~p is true (T).
- q is true (T).
- (~p q) means "not p or q", which is true (T) if at least one of p or q is true. In this case, q is true, so (~p q) is true.
- r is false (F).
- Finally, the whole expression is a conjunction (and) of (~p q) and r, meaning that it is true only if both (~p q) and r are true. However, since r is false, the entire expression must be false.
To see why, let's break down the expression:
- ~p means "not p", so if p is false (F), then ~p is true (T).
- q is true (T).
- (~p q) means "not p or q", which is true (T) if at least one of p or q is true. In this case, q is true, so (~p q) is true.
- r is false (F).
- Finally, the whole expression is a conjunction (and) of (~p q) and r, meaning that it is true only if both (~p q) and r are true. However, since r is false, the entire expression must be false.
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Let p, q and r be three logical statements with truth values F, T and F respectively, then the truth value of (~ p ⇒ ~ q) v r isa)Tb)F, if r had truth value Tc)Fd)F, if q had truth value FCorrect answer is option 'C'. Can you explain this answer?
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