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

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

Consider three statements p: Person ‘A’ passed in mathematics exam...

Consider three statements
p:p: Person ‘A’‘A’ passed in mathematics exam
q:q: Person ‘A’‘A’ passed in physics exam
r:r: Person ‘A’‘A’ passed in chemistry exam
Then, the statement \left(\left( \left(p ⇒ q\right)\right) ⇒ r\right) is equivalent to

Options

  1. APerson AA passed only in mathematics among mathematics & physics & chemistry.
  2. BPerson AA failed only in mathematics among mathematics & physics & chemistry.
  3. CPerson AA passed in all the three subjects mathematics & physics & chemistry.
  4. DPerson AA passed in chemistry but failed in mathematics & physics.

Correct answer

A. Person AA passed only in mathematics among mathematics & physics & chemistry.

Step-by-step solution

 (( (p⇒q))⇒r)≡ (p∧ q)⇒r~ \left(\left(~ \left(p ⇒ q\right)\right) ⇒ r\right) ≡ ~ \left(p ∧ ~ q\right) ⇒ r
≡p∧ q∧ r≡p∧ (q∨r)≡onlyp\begin{array}{ll}≡ p ∧ ~ q ∧ ~ r ≡ p ∧ ~ \left(q ∨ r\right) \\ ≡ onlyp\end{array}
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