How to prove the 2 nd part tof the problem.Independent proof is possible but here it is given that we will have to prove it from the previous result.I was able to do 1 st part only.The things that I observed is i(pi) + i(sigma) and i(pi • sigma) is of same parity.But could not prove it .if anyway we can can prove that we r done.I am asking for an easy approach to 2nd part .Any help would be appreciated.Thanks in advance.
2026-03-25 06:08:33.1774418913
how to prove homomorphism
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Note that for any two sets $A,B$, $$\left|A\Delta B\right|=\left|A\right|+\left|B\right|-2\left|A\cap B\right|.$$ This means that $$\left(-1\right)^{\left|A\Delta B\right|}=\left(-1\right)^{\left|A\right|}\cdot \left(-1\right)^{\left|B\right|}.$$
Can you see how to continue?