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

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

The statement p ⇔ q is not equivalent to

The statement p⇔qp ⇔ q is not equivalent toThe statement p ⇔ q is not equivalent toThe statement p ⇔ q is not equivalent toThe statement p ⇔ q is not equivalent to

Options

  1. A(p∨q)⇒(p∧q)\left(p ∨ q\right) ⇒ \left(p ∧ q\right)
  2. B(p∧q)⇒(p∨q)\left(p ∧ q\right) ⇒ \left(p ∨ q\right)
  3. C(p∨q)⇔(p∧q)\left(p ∨ q\right) ⇔ \left(p ∧ q\right)
  4. D(p∨q)∨(p∧q)\left(p ∨ q\right) ∨ \left(p ∧ q\right)

Correct answer

B. (p∧q)⇒(p∨q)\left(p ∧ q\right) ⇒ \left(p ∨ q\right)

Step-by-step solution

(A)(p∨q)⇒(p∧q)<br/><imgsrc="/api/proxy−image?url=https\left(A\right) \left(p ∨ q\right)⇒ \left(p ∧ q\right)<br /><img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fnta_abhyas%252Fjee_main%252Fimages%252Fc835a6e3-4ec1-44ed-af5e-af4996b86232.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2Fc835a6e3-4ec1-44ed-af5e-af4996b86232.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2Fc835a6e3-4ec1-44ed-af5e-af4996b86232.png?alt=media" style="width:1.67986in;height:0.77361in" /> which is same asp ⇔ q<br/>(B)(p∧q)⇒(p∨q)istautologybecause(p∧q)issubset<br /> \left(B\right)\left(p ∧ q\right)⇒ \left(p ∨ q\right) is tautology because \left(p ∧ q\right) is subset of \left(p ∨ q\right)
\left(C\right) \left(p ∨ q\right)⇔(p∧q)⇔ \left(p ∧ q\right)
The statement p ⇔ q is not equivalent to which is same as p⇔qp ⇔ q
\left(D\right)\left(p ∨ q\right)∨(p∧q)∨ \left(p ∧ q\right)
The statement p ⇔ q is not equivalent to which is same as p⇔qp ⇔ q
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