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$\cap$C=null set.
But A\B$\cap$C=(B$\cap$C)\A
∴(B$\cap$C)\A=null set.
Which means (B$\cap$C)=A
Since x$\in$A, x$\in$(B$\cap$C)
Hence if x$\in$C, then x$\in$B

 

[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.