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

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

If p: " 4 is an odd number" and q: " 4 ^ 3 is an even number" are...

If p:p: "44 is an odd number" and q:q: "43isanevennumber"aretwostatements,thenwhichofthefollowingstatementsisequivalentto{4}^{3} is an even number" are two statements, then which of the following statements is equivalent to∼ (p⇒q)?\left(p ⇒ q\right)?

Options

  1. A"44 is an odd number and 43{4}^{3} is an even number"
  2. BThe negation of the statement "44 is not an odd number or 43{4}^{3} is not an even number"
  3. CBoth ("44 is an odd number and 43{4}^{3} is an even number") and (The negation of the statement "44 is not an odd number or 43{4}^{3} is not an even number")
  4. D"44 is an odd number and 43{4}^{3}& is not an even number"

Correct answer

D. "44 is an odd number and 43{4}^{3}& is not an even number"

Step-by-step solution

∼(p⇒q)≡∼(∼p∨q)≡(p∧∼q)∼ ( p ⇒ q ) ≡ ∼ \left(∼ p ∨ q\right) ≡ \left(p ∧ ∼ q\right)

Hence, the equivalent statement of ∼(p⇒q)∼ \left(p ⇒ q\right) is ''44 is an odd number and 43{4}^{3}& is not an even number''
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