Create a table that lists all the possible input combinations for 4 Boolean variables. Write the existential quantification that claims a value exists that will make the sum of the squares of two numbers a negative value. Indicate whether or not the quantification is true. Write the universal quantification that claims the sum any number x and the next consecutive number is greater than two times x.

There is a positive integer that is divisible by every prime number. Symbolize the above statement using two quantifiers. Define the domains and any predicates that you used.

Analyze and answer the following statements. 1. State whether each bi-conditional is true or false. a. x> 7 if and only if x > 6 b. x+ 5 > 7 if and only if > 2 2. Use p, q, and r as defined in Example 6. Write the following symbolic statements in words: a. p A ^~r b. ~q 4 ^r 3. Write the negation of each conditional statement. a. If I finish the report, I will go to the concert. b. If the square of n is 25, then n is 5 or – 5. 4. Write each of the following in its equivalent disjunctive form. a. If I don't move to Georgia, I will live in Houston. b. If the number is divisible by 2, then the number is even. 5. Construct a truth table for [p ^ (p → q)] – q. 6. Determine the truth value of each of the following conditional statements. a. If 4 > 3, then 2 +5 = 6 b. If 5 > 9, the 4 > 9 c. If Tuesday follows Monday, then April follows march. 7. Identify the antecedent and consequent in each of the following conditional statements. a. If I study for at least 6 hours, then I will get an A on…

why don't we use the existential instantiation(∃x) instead of the universal because it says "A car" which means there exists one in the domain.