Answer
a. p → q
b. r ∨ s
c. ∼s → ∼t
d. ∼q ∨ s
e. ∼s
f. ∼p ∧ r → u
g. w ∨ t
h. ∴ u ∧ w
d. ∼q ∨ s
e. ∼s
∴ ∼q (1) Elimination
a. p → q
∼q (1)
∴ ∼p (2) Modus Tollens
c. ∼s → ∼t
e. ∼s
∴ ∼t (3) Modus ponens
g. w ∨ t
∼t (3)
∴ w (4) Elimination
b. r ∨ s
e. ∼s
∴ r (5) Elimination
r (5)
∼p (2)
∴ ∼p ∧ r (6) Conjunction
f. ∼p ∧ r → u
∼p ∧ r (6)
∴ u (7) Modus Ponens
w (4)
u (7)
∴ u ∧ w Conjunction = h
Work Step by Step
first step : by using (d)and (e ) as premises then the conclusion will be ∼q (1) by Elimination
2nd step: by using (a)and (1) as premises then the conclusion will be ∼p (2) by Modus Tollens
3rd step : by using (c)and (e) as premises then the conclusion will be ∼t (3) by Modus Tollens
4th step: by using (g)and (3) as premises then the conclusion will be w (4) by Elimination
5th step : by using (b)and (e) as premises then the conclusion will be r (5) by Elimination
6th step: by using (5)and (2) as premises then the conclusion will be ∼p ∧ r (6) by Conjunction
7th step: by using (f)and (6) as premises then the conclusion will be u (7) by Modus Ponens
8th step: by using (4)and (7) as premises then the conclusion will be u ∧ w by Conjunction
