Question
All poor people are merciful.
All beggars are poor.
$\therefore$ All beggars are merciful.
All beggars are poor.
$\therefore$ All beggars are merciful.

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| (1) E v (E & Q) | P |
| (2) E $\rightarrow$ L | P |
| (3) ~L | P/ $\therefore$ Q v M |
| (4) ~ E | ................ |
| (5) E & Q | ................ |
| (6) Q | ................ |
| (7) Q v M | ................ |
| (1) A $\rightarrow$ B | P |
| (2) C $\rightarrow$ D | P |
| (3)~ D & ~ B | P/$\therefore$(~ A & ~ C) v P |
| (4) ~ B | ................ |
| (5) ~ A | ................ |
| (6) ~ p | ................ |
| (7) ~ c | ................ |
| (8) ~A & ~ C | ................ |
| (9)( ~ A & ~ C) v P | ................ |