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The statement $$(p \wedge q) \Rightarrow(p \wedge r)$$ is equivalent to :

JEE · Math · previous-year question

  1. A.$$q \Rightarrow(p \wedge r)$$
  2. B.$$p\Rightarrow(\mathrm{p} \wedge \mathrm{r})$$
  3. C.$$(\mathrm{p} \wedge \mathrm{r}) \Rightarrow(\mathrm{p} \wedge \mathrm{q})$$
  4. D.$$(p \wedge q) \Rightarrow r$$correct

Answer

D. $$(p \wedge q) \Rightarrow r$$

Explanation

.tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-baqh{text-align:center;vertical-align:top} $$p$$ $$q$$ $$r$$ $$A = p\, \wedge q$$ $$B = p\, \wedge r$$ $$A \to B$$ $$q \to B$$ $$p \to B$$ $$B \to A$$ $$A \to r$$ T T T T T T T T T T T F T F T T T T F T F T T F F T F T T T F F T F F T T T T T T T F T F F F F T F T F F F F T T F T T F T F F F T F T T T F F F F F T T T T T $$(p\, \wedge \,q) \Rightarrow (p\, \wedge \,r)$$ is equivalent to $$(p\, \wedge \,q) \Rightarrow r$$

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