Question

If A = {a,b), B =
(x,y) and C = {a, c, y), then verify Ax(BUC) = (AXB)U(AXC)
AX(BOC)=(
AB) n(AXC) and (B-C) A = (Bx A) - (CxA)​

please answer this question
I have my exams revision after answering this question

Answer 1

Step-by-step explanation:

#############################

HOPE IT MAY HELP YOU

############################

Answer 2

Given:

A = {a,b}

B ={x,y}

C = {a, c, y}

To Find:

Ax(BUC) = (AxB)U(AxC)

Ax(B∩C)=(AxB)∩(AxC)

(B-C) A = (BxA) - (CxA)​

Solution:

i) Ax(BUC) = (AxB)U(AxC)

LHS = Ax(BUC)

       = {a,b} x {x,y,a,c,}

       = {(a,x),(a,y),(a,a),(a,c),(b,x),(b,y),(b,a),(b,c)}

RHS = (AxB)U(AxC)

        ={(a,x),(a,y),(b,x),(b,y)} U {(a,a),(a,c),(a,y),(b,a),(b,c),(b,y)}

        ={(a,x),(a,y),(a,a),(a,c),(b,x),(b,y),(b,a),(b,c)}

LHS = RHS

ii) Ax(B∩C)=(AxB)∩(AxC)

LHS = Ax(B∩C)

        = {a,b}x{y}

        = {(a,y),(b,y)}

RHS = (AxB)∩(AxC)

        = {(a,x),(a,y),(b,x),(b,y)} ∩ {(a,a),(a,c),(a,y),(b,a),(b,c),(b,y)}

        = {(a,y),(b,y)}

LHS = RHS

iii) (B-C) A = (BxA) - (CxA)​

LHS = (B-C) A

       = {x} x {a,b}

       = {(x,a),(x,b)}

RHS = (BxA) - (CxA)​

       = {(x,a),(x,b),(y,a),(y,b)} ∩ {(a,a),(a,b),(c,a),(c,b),(y,a),(y,b)}

       = {(x,a),(x,b)}

LHS = RHS

Hence, verified

#SPJ2