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9. (10 ) Suppose that H and K are distinct subgroups of G of index 2. Prove that HnK is a normal subgroup of G of index 4 and

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Sne,G H1 - 2 omd L 6 K] 2, both H amd K tonaknnr narmal G. tHence ane HK a n HK renton beth Hnd Nand H and K bsth dintn H H L

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