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JEE Main 2008
Exam
JEE Main
Year
2008
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2008 · Mathematics · Mathematical Reasoning

The statement p arrow(q arrow p) is equivalent to

The statement p→(q→p)p \rightarrow(q \rightarrow p) is equivalent to

Options

  1. Ap→(p→q)p \rightarrow(p \rightarrow q)
  2. Bp→(p∨q)p \rightarrow(p \vee q)
  3. Cp→(p∧q)p \rightarrow(p \wedge q)
  4. Dp→(p↔q)p \rightarrow(p \leftrightarrow q)

Correct answer

B. p→(p∨q)p \rightarrow(p \vee q)

Step-by-step solution

p→(q→p)=∼p∨(q→p)=∼p∨(∼q∨p) since p∨∼p is  always  true  =∼p∨p∨q=p→(p∨q).\begin{aligned}& p \rightarrow(q → p)=\sim p \vee(q → p) \\ & =\sim p \vee(\sim q \vee p) \quad \text{ since }p\vee \sim p \text{\text{ is }\text{ always }\text{ true } }\\ & =\sim p \vee p \vee q=p \rightarrow(p \vee q) . \end{aligned}
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