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a. Write the following statements using and find the negation, the converse, the Inverse and the contrapositive If a natural number is even then it is divisible by two. Translate into symbols the following compound statement and give the form of the Compound statement. In each case, list the statements P, Q, R... b. If x is odd and y is odd then (x+1) is even and (y+1) is odd. c. It is raining but it is not hot.

a. Write the following statements using and find the negation, the converse, the Inverse and the contrapositive If a natural number is even then it is divisible by two. Translate into symbols the following compound statement and give the form of the Compound statement. In each case, list the statements P, Q, R... b. If x is odd and y is odd then (x+1) is even and (y+1) is odd. c. It is raining but it is not hot.

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a. Write the following statements using and find the negation, the converse, the Inverse and the contrapositive If a natural number is even then it is divisible by two. Translate into symbols the following compound statement and give the form of the Compound statement. In each case, list the statements P, Q, R... b. If x is odd and y is odd then (x+1) is even and (y+1) is odd. c. It is raining but it is not hot.

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Consider the following statement. If x is nonnegative, then x is positive or x is 0. In (a)-(d) below, select the negation, contrapositive, converse, and inverse for the statement. (Assume that all variables represent fixed quantities or entities, as appropriate.) (a) Negation If x is not positive and x is not 0, then x is not nonnegative. If x is positive or x is 0, then x is nonnegative. If x is not nonnegative, then both x is not positive and x is not 0. If x is not nonnegative, then x is positive or x is 0. x is nonnegative and x is not positive and x is not 0. (b) Contrapositive If x is not positive and x is not 0, then x is not nonnegative. If x is positive or x is 0, then x is nonnegative. If x is not nonnegative, then both x is not positive and x is not o. If x is not nonnegative, then x is positive or x is 0. x is nonnegative and x is not positive and x is not 0. (c) Converse If x is not positive and x is not 0, then x is not nonnegative. If x is positive or x is 0, then x is nonnegative. If x is not nonnegative, then both x is not positive and x is not 0. If x is not nonnegative, then x is positive or x is 0. x is nonnegative and x is not positive and x is not 0. (d) Inverse If x is not positive and x is not 0, then x is not nonnegative. If x is positive or x is0, then x is nonnegative. If x is not nonnegative, then both x is not positive and x is not 0. If x is not nonnegative, then x is positive or x is 0. x is nonnegative and x is not positive and x is not 0.
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