First slide

Introduction to mathematical reasoning

Question

The statement $A \to (B \to A)$ is equivalent to:

Moderate

A

$A \to (A \land B)$
B

$A \to (A \to B)$
C

$A \to (A \lor B)$
D

$A \to (A \leftrightarrow B)$

Solution

$\begin{array}{l} Given statement: A ⟶ (B \to A) \\ ≃ ~ A \lor (B \to A) \\ ≃ ~ A \lor (~ B \lor A) ∣ \\ ≃ (~ A \lor A) \lor B \\ ≃ t \lor B ≃ t \\ (3) \Rightarrow A \to (A \lor B) ≃ ~ A \lor (A \lor B) \\ ≃ (~ A \lor A) \lor B \\ ≃ & \approx t \lor B \\ ≃ t \end{array}$

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