In this exercise we show that the meet and join operations are commutative. Let A and B be m × n zero – one matrices. Show thata) A ? B = B ? A.________________b)B ? A = A ? B.

Solution:Step1Given that Let A and B be m × n zero – one matrices.Step2To findShow thata) A B = B A.b)B A = A B.Step3A zero–one matrix:-A matrix is in rectangular form with entries 0 or 1.a) A B = B A.Here,L.H.S(Left hand side)=R.H.S(right hand side)=Let L.H.S= = We know thatBy using this we getL.H.S = R.H.S= = We know thatBy using this we get = Therefore, L.H.S=R.H.STherefore, the meet and join operations are commutative. Step4b)B A = A B.Here,L.H.S(Left hand side)=R.H.S(right hand side)=Let L.H.S= = We know thatBy using this we getL.H.S = R.H.S= = We know thatBy using this we get = Therefore, L.H.S=R.H.STherefore, the meet and join operations are commutative.