Let the domain be the set of all animals. Define the following predicates: A(x) : x can add. W(x) : x can waltz. • D(x) : x is a dog. • C(x) : x is a cat. Translate each of the following logical expressions into English. 1. Vx(D(x) → (A(x) v W(x)). 2. Ex(C(x) A ¬A(x) A W(x)) 3. ¬3x(D(x) A A(x)) 4. Vx((D(x) V C(x)) → W(x))

Let r represent "I get an A," let p represent "The taxes are high," and let q represent "The job pays well." Write the following compound statement in symbols. The job pays well, and if the taxes are high, then I do not get an A. Choose the correct symbolic form below. O A. q^(p-r) O B. (q→p) ^~ OC. q^(-pr) OD. q→ (p^r)

Are the following statement forms logically equivalent? p V q →~ p and pV ((p^ g)^ ~ g) O The statement forms are logically equivalent. O The statement forms are not logically equivalent.

a. Construct an interpretation (i.e., give the domain and the meaning of P(x)) in which (∀x)P(x) has the value true.b. Construct an interpretation in which (∀x)P(x) has the value false.c. Can you find one interpretation in which both (∀x)P(x) is true and (∃x)P(x) is false?d. Can you find one interpretation in which both (∀x)P(x) is false and (∃x)P(x) is true?

I have to enter the letter corresponding with the statement.

The table below shows the values of predicates P(x,y) for every possible combination of values of the variables x and y. The row number indicates the value for x and the column number indicates the value for y. The domain for x and y is {1,2, 3, 4}. Ex: P(3, 1) is true because the entry in row 3, column 1 is T. P 1 2 3 4 1 F F T F 2 FFT F 3 T TT F 4 T FT F Determine the truth value of each expression. (1) Væ P(x, 4) (2) Vy P(1, y) (3) Jx P(x, 3) Pick + Pick + Pick + (4) Ey P(3, y) Pick +

Let P(x) denote the statement "x is taking Math 111s". The domain of discourse is the set of all students. Write the following in words. 1. VxP(x) 2. Зх-Р(х) 3. ЭХР(x)

buy A. Determine whether the following statements are always true, sometimes true. or never true. the Easy Milk Tea w its should 1. Itx-25-0, then x-5. 2 Ifx-27-0, then x-3 3. If 5x -45-0, then x-9. Ifx 10x--25, then x--5. 5. Ifx-3x+ 3x-1-64, then x-5. The Zero Product Property states that: If a and b are expressions, and ab-0, then a-0. 7. If the product of two numbers is zero, then at least one of 8. According to the Zero Product Property, If a and b are expressions, and ab-0, then b-0. the numbers is zero. ey Ma 10. In solving an equation by factoring, one side of the equation must be zero. 9. If (x+1) (xr+ 2)-12, then x+1-12 or a+2-12.

Please help me with these question. I am having trouble understanding what to do

Please number 3 use number 2 info