Suppose that A\B is disjoint from C and x εA.prove that if xεC then xε

[bean29]

Suppose that A\B is disjoint from C and x εA.prove that if xεC then xεB

 

[Abhilash H N]

Given A\B is disjoint from C.
i.e, A\B\capC=null set.
But A\B\capC=(B\capC)\A
∴(B\capC)\A=null set.
Which means (B\capC)=A
Since x\inA, x\in(B\capC)
Hence if x\inC, then x\inB

 

[verty]

Proof by contrapositive works here, very well in fact.

 

[mfb]

This is not an acceptable way to ask for help at homework problems. In addition, it is in the wrong forum.