Q. The statement $B \Rightarrow((\sim A ) \vee B )$ is equivalent to:
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
T
T
T
T
T
T
T
T
T
T
F
T
T
T
| 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 | T | T | T | T |
| T | T | T | T | T |
| T | F | T | T | T |