## Proof with Sets

If C is a subset of A and D is a subset of B, then C or D is a subset of A or B

• Assume A is not a subset of C or B is not a subset of D. There exists an 'a' which is an element of A but is not an element of C and there exists a 'b' that is an element of B but not an element of D. 'a,b' is an element of A x B but 'a,b' is not an element of C x D. Therefore, A x B is not a subset of C X D. Thus, by contraposition, if A x B is a subset of C x D then A is a subset of C and B is a subset of D.
• Anonymous commented

What is AXB mean?

• let us suppose C or D is not a subset of A or B
=> C or D contains some elements which are not present in A or B
i.e,both C and D contains some elements which are not present in A or B
i.e C contains some elements which are not present in A
and D contains some elements which are not present in B
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