Fsc Part 1 Mathematics (Complete Solution)

Q5
Prove that p∨(∼p∧∼q)∨(p∧q)=p∨(∼p∧∼q)

Solution:

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

The last two columns of the above table show that the statements p∨(∼p∧∼q)∨(p∧q) and p∨(∼p∧∼q) are equivalent to each other. So p∨(∼p∧∼q)∨(p∧q)=p∨(∼p∧∼q) hence proved..

Other Topics

;