1. Suppose your friend is thinking of a number between 10 and 1,000,000. Suppose

Question

1. Suppose your friend is thinking of a number between 10 and 1,000,000. Suppose that P "Your number is prime". Q = "Your number is even", and R = "Your number is evenly divisible by an integer other than 1 and itself. S = "Your number is odd". For each of the implications below do the following: Insert one or more logical operators such as:- true statements about the number. Write the answer from i. above in English. i. v, and/or. to construct ii. Given your answers for i. above, can any of the implications be replaced with and the statement still be true? Justify your answer. For instance, if you're given 0-P. Since an even number is not prime, the negation operator would need to be inserted before Q for the statement to be true, therefore the correct implication would be Q-P. The English statement would be "If your number is even then it is not prime" The implication cannot be replaced by because-I-Q is not always true. even. ii. iii. For instance, 15 is not prime and it's not

Explanation / Answer

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Solution:

i) Expression: P=> Q v S

ii) English statement: "If your number is prime then it will either be odd or even."

iii) The implication cannot be replaced by <=> because Q v S => P is not always true.

For instance, 4 and 9 are even and odd numbers and they are not prime.

Like that you can also think of some logical expressions.

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