Fsc Part 1 Mathematics (Complete Solution)

Q4
Determine whether each of the following is a tautology, a contingency or an absurdity

(i) p∧∼p

Solution:

p∼pp∧∼p
T F F
F T F

The last column shows that p→(q→p) is false for all values, so it is a absurdity.

(ii) p→(q→p)

Solution:

pqq→pp→(q→p)
T T T T
T F T T
F T F T
F F T T

The last column shows that p→(q→p) is true for all values, so it is a tautology.

(iii) q∨(∼q∨p)

Solution:

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

The last column shows that q∨(∼q∨p) is true for all values, so it is a tautology`.

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