Fsc Part 1 Mathematics (Complete Solution)

Q3
Show that each of the following statements is a tautology

(i) (p∧q)→p

Solution:

pqp∧q(p∧q)→p
T T T T
T F F T
F T F T
F F F T

The column of table shows that the statement (p∧q)→p is true for all values,so it is a tautology.

(ii) p→(p∨q)

Solution:

pqp∨qp→(p∨q)
T T T T
T F T T
F T T T
F F F T

The column of table shows that the statement p→(p∨q) is true for all values,so it is a tautology.

(iii) ∼(p→q)→p

Solution:

pqp→q∼(p→q)∼(p→q)→p
T T T F T
T F F T T
F T T F T
F F T F T

The column of table shows that the statement ∼(p→q)→p is true for all values,so it is a tautology.

(iv) ∼q∧(p→q)→∼p

Solution:

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

The column of table shows that the statement ∼q∧(p→q)→∼p is true for all values,so it is a tautology.

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