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

Solution:Step1Given thatLet A,B, and C be m × n zero–one matrices.Step2To findShow thata) (A B) C = A (B C).b) (A B) C = A (B C).Step3a) (A B) C = A (B C).Here,L.H.S(Left hand side)=R.H.S(right hand side)=A (B C)Let L.H.S= = We know thatBy using this we getL.H.S= R.H.S=A (B C) = = = So, L.H.S=R.H.STherefore, the meet and join operations are associative. (A B) C = A (B C)Step4b) (A B) C = A (B C).Here,L.H.S(Left hand side)=R.H.S(right hand side)=A (B C)Let L.H.S= = We know thatBy using this we getL.H.S= R.H.S=A (B C) =A = We know thatBy using this we getR.H.S= So, L.H.S=R.H.STherefore, the meet and join operations are associative. (A B) C = A (B C).