1. Given that (G,*) is a group and that H and K are subgroups of (G,*), show that the set formed by the intersection of H and K is also a subgroup of (G,*).

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A: 6. Start with the power rule in logarithm1st term2nd term3rd termUsing this expressionWe use the...

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A: Let P(n) be the predicate, '1+2+2^2 +...+2^n = 2^(n+1) - 1'.

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A: For the first constraint: x1​−4x2​≥5⟹if x2​=0, then x1​≥5. For the second constraint: x1​−3x2​≤1⟹if...