Question

If A={a,b,c,d,e},B={a,c,e,g} and C={b,e,f,g},verify that
1) AUB=BUA
2) AUC=CUA

Answer 1

Answer:

AUB={a,b,c,d,e}U{a,c,e,g}

={a,b,c,d,e,g}

BUA={a,c,e,g}U{b,e,f,g}

={a,b,c,e,f,g}

Answer 2

Hello, Buddy!!

✰ Given:-

• A = {a,b,c,d,e}
• B = {a,c,e,g}
• C = {b,e,f,g}

✰ To Prove:-

• AUB = BUA
• AUC = CUA

✫ Required Proof:-

Now, AUB

→ {a,b,c,d,e}U{a,c,e,g}

→ {a,b,c,d,e,g}

• AUB = {a,b,c,d,e,g}

BUA

→ {a,c,e,g}U{a,b,c,d,e}

→ {a,c,e,g,b,d}

• BUA = {a,b,c,d,e,g}

Hence, Proved. ➪ AUB = BUA

Now, AUC

→ {a,b,c,d,e}U{b,e,f,g}

→ {a,b,c,d,e,f,g}

• AUC = {a,b,c,d,e,f,g}

CUA

→ {b,e,f,g}U{a,b,c,d,e}

→ {b,e,f,g,a,c,d}

• CUA = {a,b,c,d,e,f,g}

Hence, Proved. ➪ AUC = CUA

$\boxed{\tt{@MrSovereign}}$

Hope This Helps!!