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The statement \(B\Rightarrow ((~A)∨B)\) is not equivalent to : [JEE Main 2023, 29 Jan (Shift 2)]

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The statement \(B\Rightarrow ((~A)∨B)\) is not equivalent to :

[JEE Main 2023, 29 Jan (Shift 2)]

a

\(B\Rightarrow ((~A)\Rightarrow B)\)

b

\(A\Rightarrow ((~A)\Rightarrow B)\)

c

\(A\Rightarrow (A\Leftrightarrow B)\)

d

\(B\Rightarrow (A\Rightarrow B)\)

✓ Correct answer: c)

\(A\Rightarrow (A\Leftrightarrow B)\)

Explanation

\(\begin{matrix}\mathrm{A} & \mathrm{B} & ~\mathrm{A} & ~\mathrm{A}∨\mathrm{B} & \mathrm{B}\Rightarrow ((~\mathrm{A})∨\mathrm{B}) & ~\mathrm{A}\Rightarrow \mathrm{B} & \mathrm{A}\Rightarrow \mathrm{B} & \mathrm{A}\Leftrightarrow \mathrm{B} & 1 & 2 & 3 & 4 \\ \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\ \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T}\end{matrix}\)
1,2 and 4 are correct option.

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