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For any sets A ,B ,C ,D prove that: (Axx...

For any sets `A ,B ,C ,D` prove that: `(AxxB)nn(CxxD)=(AnnC)xx(BnnD)`

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The correct Answer is:
N/a
Let `(a,b) in (AxxB) nn (CxxD)`
`implies (a,b) in (AxxB) and (a,b) in (C xx D)`
`implies (a in A and B in B) and (a in C and b in D)`
`implies (a in A and a in C) and (a in C and B in D)`
`implies a in (A nn C) and b in (B nn D)`
`implies (a,b) in (A nn C) xx (B nn D).`
` therefore (AxxB) nn (C xx D) sube (A nn C) xx (B xx D) " "...(1)`
Similarly,
`(A nn C) xx( B nn D) sube (A xx B) nn( C xx D) " "...(2)`
Now, from eqs. (1) and (2)
`(AxxB) nn (CxxD) =(Ann C) xx(B nn D).`
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