Mathematical Reasoning Question 6
Question 6 - 29 January - Shift 2
The statement $B \Rightarrow((\sim A) \vee B)$ is equivalent to
(1) $B \Rightarrow(A \Rightarrow B)$
(2) $A \Rightarrow(A \Leftrightarrow B)$
(3) $A \Rightarrow((\sim A) \Rightarrow B)$
(4) $B \Rightarrow((\sim A) \Rightarrow B)$
Show Answer
Answer: (2)
Solution:
| $A$ | $B$ | $\sim A$ | $\sim A \vee B$ | $B \Rightarrow((\sim A) \vee B)$ |
|---|---|---|---|---|
| $T$ | $T$ | $F$ | $T$ | $T$ |
| $T$ | $F$ | $F$ | $F$ | $T$ |
| $F$ | $T$ | $T$ | $T$ | $T$ |
| $F$ | $F$ | $T$ | $T$ | $T$ |
| $A \Rightarrow B$ | $\sim A \Rightarrow B$ | $B \Rightarrow$ $(A \Rightarrow B)$ |
$A \Rightarrow$ $((\sim A) \Rightarrow B)$ |
$B \Rightarrow$ $((\sim A) \Rightarrow B)$ |
|---|---|---|---|---|
| $T$ | $T$ | $T$ | $T$ | $T$ |
| $F a t$ | $T$ | $T$ | $T a t$ | $T$ |
| $T$ | $T$ | $T$ | $T$ | $T$ |
| $T$ | $F$ | $T$ | $T$ | $T$ |
