Which of the following are propositions? a. All dogs have tails. b. My little sister is cute. c. Today it is snowing here.

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A: The complete solution is in below

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A: We have to check the given function is continuous at x=0.

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Q: 5. Write the formal proof that 2"+2 + 32n+1 is divisible by 7 for all positive integers.

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A: Use the definition of terminal point, we solve this problem as in next step.

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A: Here we use basic definition of continuous function.

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A: As we know  P(n, k) = (n!) /(n-k)!  

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A: Please find attachment for the details solution

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Q: 4x1 + x2 - X3 x1 + 6x, - 2x3 + x4 - X5 3 -6 X2 + 5x3 2x2 Xs + X6 -5 + 5x4 X5 X, - Xg -X3 - X4 + 6x5 ...

A: We can solve this by using elimination method

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Q: 5. Write the formal proof that 2"+2 + 32n+1 is divisible by 7 for all positive integers.

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