Prob. Show that-
(P∩Q)X(R∩S) = (PXR)∩(QXS)
For some arbitrary sets P, Q, R and S
Solution:
Consider(x,y)
(x,y)∈(P∩Q)X(R∩S)
x∈(P∩Q) ∧ y∈(R∩S)
(x∈P and x∈Q) ∧ (y∈R and y∈S)
(x∈P ∧ y∈R) and (x∈Q ∧ y∈S)
(x,y)∈(P∧R) and (x,y)∈Q∧S)
(x,y)∈((P∧R) and (Q∧S))
(x,y)∈((P×R) ∩ (Q×S))
(PXR)∩(QXS)