Question

If A ={a,b,c,d,e},B={a,c,e,g}andC={b,e,f,g}, verify that: A intersection(B-C)=(A intersection B)-(A intersection C)

Answer 1

A intersection (B-C)=(A intersection B)-(A intersection C)
A={a b c d e}
B={a c e g}
C={b e f g}
now find L H S part
= {a b c d e} intersection ({a c e g}-{b e f g})
={a b c d e} intersection ({a c})
={a b c d e} intersection { a c}
={a c}
LHS={a c}
now RHS
=({a b c d e}intersection {a c e g})-({a b c d e} intersection {b e f g}
={a c e}-{b e}
={a c}
so LHS=RHS