What are the truth values of (∼ p ⇒ ∼ q) and (∼ p ⇒ q) respectively, when p and q always speak the truth in any argument?

Correct answer: A. T, T Since, truth value of p is T and truth value of q is also T So,~ ~ p is always false, therefore~(∼ p ⇒ ∼ q) and (∼ p ⇒ q) are always true (since,~ p ⇒ q is false only when p is true and q is false )

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Mathematical Reasoning

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

What are the truth values of (∼ p ⇒ ∼ q) and (∼ p ⇒ q)...

What are the truth values of

\left(∼ p ⇒ ∼ q\right)

and

\left(∼ p ⇒ q\right)

respectively, when

p and q

always speak the truth in any argument?

Options

A $T, T$
B $F, F$
C $T, F$
D $F, T$

Correct answer

A. $T, T$

Step-by-step solution

Since, truth value of

p

T

and truth value of

q

is also

T

So,~

~ p

is always false, therefore~\left(∼ p ⇒ ∼ q\right)

and \left(∼ p ⇒ q\right)

are always true

(since,~

p ⇒ q

is false only when

p

is true and

q

is false

)

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