Question
Consider the following two propositions: P _1: (p q) P_2:(p q) (( p) q) If the proposition p (( p) q) is evaluated as FALSE, then :
BITSAT
Mathematics
Mathematical Reasoning
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. P_1 is TRUE and P_2 is FALSE
- B. P _1 is FALSE and P _2 is TRUE
- C. Both P_1 and P_2 are FALSE
- D. Both P_1 and P_2 are TRUE
Answer
C. Both P_1 and P_2 are FALSE
Step-by-step solution
Given propositions P _1: ( p q ) P _2:(p q) (( p) q) Required table is shown below. \( array |l|l|l|l|l|l|l|l|l|l|l| p & q & p & q & p q & p ( (p q) & p q & (p q) & p q & p_2 \\ T & T & F & F & T & T & F & T & F & F \\ T & F & F & T & F & F & T & F & T & F \\ F & T & T & F & T & T & T & F & F & F \\ F & F & T & T & T & T & T & F & F & F \\ array \) \(p ( p q)\) is \(F\) when \(p\) is true \(q\) is false From table \(P_1 ~\&~ P_2\) both are false
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