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

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

Let p, q ~and& r be three statements, then (p → q) → r is...

Let p,qp, q~and& rr be three statements, then \left(p \to q\right) \to r is equivalent to

Options

  1. A(p∨r)∧(q∨r)\left(p ∨ r\right) ∧ \left(q ∨ r\right)
  2. B(p∨r)∧(q∨r)\left(p ∨ r\right) ∧ \left( q ∨ r\right)
  3. C(p∧r)∨(q∨r)\left(p ∧ r\right) ∨ \left(q ∨ r\right)
  4. D(p∨q)→r\left(p ∨ q\right) \to r

Correct answer

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

Step-by-step solution

\left(p \to q\right)\to r ≡ \left( p ∨ q\right)\to r<br/><br/>≡ \left( p ∨ q\right)∨r∨ r
≡(p∧q)≡ \left(p ∧ q\right)∨ r<br/><br/>≡ \left(p ∨ r\right)∧(q∨r)∧ \left( q ∨ r\right)
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