Fsc Part 1 Mathematics (Complete Solution)

Q2
Contruct truth tables for the following statements

(i) (p→∼p)∨(p→q)

Solution:

pq∼pp→∼pp→q(p→∼p)∨(p→q)
T T F F T T
T F F F F F
F T T T T T
F F T T T T

(ii) (p∧∼p)→q

Solution:

pq∼pp∧∼p(p∧∼p)→q
T T F F T
T F F F T
F T T F T
F F T F T

(iii) ∼(p→q)↔(p∧∼q)

Solution:

pq∼qp→q∼(p→q)p∧∼q∼(p→q)→(p∧∼q)(p∧∼q)→∼(p→q)
T T F T F F T T
T F T F T T T T
F T F T F F T T
F F T F F F T T

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