MHT CET · Maths · Mathematical Reasoning
\((p \wedge q) \vee \sim p\) is equivalent to
- A \(\sim p \wedge q\)
- B \(\sim p \vee q\)
- C \(p \wedge q\)
- D \(p \vee q\)
Answer & Solution
Correct Answer
(B) \(\sim p \vee q\)
Step-by-step Solution
Detailed explanation
\((p \wedge q) \vee \sim p=\sim p \vee(p \wedge q)\)
[By commutative law] \(\begin{array}{lr}=(\sim p \vee p) \wedge(\sim p \vee q) & \text { [By distributive law] } \\ =(p \vee \sim p) \wedge(\sim p \vee q) & \text { [By commutative law] }\end{array}\)
\(=t \wedge(\sim p \vee q)\)
[By complement law]
\(=\sim p \vee q\)
[By identity law]
[By commutative law] \(\begin{array}{lr}=(\sim p \vee p) \wedge(\sim p \vee q) & \text { [By distributive law] } \\ =(p \vee \sim p) \wedge(\sim p \vee q) & \text { [By commutative law] }\end{array}\)
\(=t \wedge(\sim p \vee q)\)
[By complement law]
\(=\sim p \vee q\)
[By identity law]
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