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BITSAT2024MathematicsMathematical ReasoningActual

Consider the following two propositions: P ₁: (p q)P₂:(p q) (( p) q) If the proposition p (( p) q) is evaluated as FALSE, then :

Options

  1. AP₁ is TRUE and P₂ is FALSE
  2. BP ₁ is FALSE and P ₂ is TRUE
  3. CBoth P₁ and P₂ are FALSE
  4. DBoth P₁ and P₂ are TRUE

Correct answer

C. Both P₁ and P₂ are FALSE

Step-by-step solution

Given propositions P ₁: ( p q ) P ₂:(p q) (( p) q) Required table is shown below. ( array |l|l|l|l|l|l|l|l|l|l|l| p & q & p & q & p q & p ( (p q) & p q & (p q) & p q & p₂ T & T & F & F & T & T & F & T & F & F T & F & F & T & F & F & T & F & T & F F & T & T & F & T & T & T & F & F & F F & F & T & T & T & T & T & F & F & F array ) (p ( p q) ) is (F ) when (p ) is true (q ) is false From table (P₁ ~ &~ P₂ ) both are false

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