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If a sum of two real numbers is less than 50, then at least one of the number is less than 25.

Prove by contraposition.

1 Answer

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Answer:

So basically you will switch the predicate and proposition (p implies q) and we will negate it so not q implies not p. So we will say that both x and y should be 25 or greater and that the sum will be 50 or greater. Below you will find the steps. I just took this course and got a 96% so i think u should get near to full points on something along the lines of this answer. The only thing u may have to change is that we should probably use k and j for x and y but off the top of my head i cannot recall exactly how to word that. Then prove using k and j but the logic is exactly the same. Its just how proofs work. Substitute in a variables for variables ..

Explanation:

Proof by contraposition : Let x and y be real numbers. Assume x is a real number greater than or equal to 25 and y is greater than or equal to 25 and the sum of x and y is greater than or equal to 50. We can then take the minimum 25 and 25 and the sum of this gives 50. This satisfies our minimum requirement of 50 since any other number combination will be above 50 we have proven by contraposition that for the sum of two real numbers x and y one number must be less than 25 to be create a sum less than 50

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