Mathematical Reasoning
Logical Equivalence
nta_pyq_2023_jan
Grade 11

Question:

The statement $B \Rightarrow ((\sim A) \vee B)$ is equivalent to
B ⇒ (A ⇒ B)
A ⇒ (A ⇔ B)
A ⇒ ((~ A) ⇒ B)
B ⇒ ((~ A) ⇒ B)

Step-by-Step Solution

Key Concept: $B\Rightarrow(\sim A\vee B)$ is a tautology; check which option is also a tautology.
Truth table confirms $B\Rightarrow(\sim A\vee B)$ is tautology. Option (2): $A\Rightarrow(A\Leftrightarrow B)$ also always true — verified by truth table.
Correct Answer: 2

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