Express the following statements in predicate logic: Some human is not mortal. For every x and every y there exists a z which is the sum of x and y. There is no prime number between 23 and 29.

3. Find the negations of each of the following statements. Is the original statement true or false? Is the negation true or false? (a) Every real number is either positive or negative. (b) There exists a positive integer n such that n is even or n2 is odd.

State the converse, contrapositive and inverse of each of these conditional statements. If it snows today I will ski tomorrow. I come to class whenever there is going to be a quiz A positive integer is a prime only if it has no divisors other than 1 and itself.

Write the following universal statement as an equivalent conditional statement in words. All even numbers are divisible by 2.

Express this in predicate logic: Each email address has exactly one email box. M(x): x is an email address B(x,y): x has an email box y

Prove the existential statement given below. There are integers c and d such that 7c + 5d 1.

Q6 Let D bethe set of all students at your school, andlet M(s) be "s is a math major."let C(s) be 's is a computer science student," andlet E(s) be 's is an engineering student. Express each of the following statements usingquantifiers, variables, and the predicates M(s).C(s) and E(s).a. There is an engineering student who is a math major.b. Every computer science student is an engineering studentc. No computer science students are engineering students.d. Some computer science students are also math majors.e. Some computer science students are engineering students and some are not