hello can you help me answer this? im really having a hard time in math please help me. Also please show solutions on how you answer these please.

III. Choose the letter of the correct/best answer.

1. Which of the following is the mathematical translation of the expression: the square of the sum of the squares of two numbers?

2. The mathematical translation of the sentence "The product of the sum and difference of two numbers is the difference of the squares of two numbers." is:

3. The mathematical translation of the phrase "a number raised to the third power increased by one" is:

4. Which of the following is the correct translation to an English phrase of the mathematical expression: ?

a. The sum of two numbers

b. The cube of the sum of two numbers

c. The sum of the cubes of two numbers

d. Two numbers raised to the third power

5. The perimeter (P) of a rectangle is twice of its length (L) and twice of its width (W). If you are going to translate this mathematically, which of the following should be the mathematical sentence?

6. Which of the following is true?

7. Which of the following is false?

d. The set of nice car is not a well-defined set.

8. Let A=

Which of the following is false?

a. C is a proper subset of A

b. C and B have at least one element in common

c. C is a subset of C

d. B is a subset of A

9. Which of the following is false?

10. Which of the following is NOT an empty set?

11. Which of the following is false?

12. Which of the following is false?

13. It is the mathematical analogue of an English noun.

a. equation c. mathematical sentence

b. expression d. equal sign

a. Cartesian product of A and B c. Union of A and B

b. Intersection of A and B d. Difference of A and B

15. Which of the following sets is a null set?

a. I and II only c. I, II and III

b. I and III only d. II and III only

16. If A is not equal to B, then which of the following is correct?

17. In a mathematical sentence 2ax + by = 6, what particular symbol is pertaining to a verb?

a. a and b c. x and y

b. 2 and 6 d. =

18. In a mathematical sentence in item number 17, the + sign is called:

a. adverb c. noun

b. connective d. pronoun

19. What property of a relation does the set of ordered pairs (1, 3), (2, 4), (1, 2), (3, 1), (4, 2), (2, 1) belong?

a. transitive c. symmetric

b. equivalence d. reflexive

20. Which of the following is NOT a function?

a. { a, b, c } c. { a, b, d }

b. { a, b, f } d. { a, b, e }

22. If U = { a, e, i, o, u}, A = { a, c, e } and B = { g, o, d }, what is A^c - B^c?

a. { a } c. { e }

b. { i } d. { o }

23. If A = {a, b}, what is A x A?

a. { a, b} c. { (a, b), (b, a), (a,a) }

b. { (a,a), (b,b)} d. { (a,a), (b,b), (a, b), (b,a)}

24. How many subsets are there in a given set A = { j, h, u, n }?

a. 16 c. 8

b. 4 d. 1

25. What is the intersection of a two sets A = {a, b, c} and B = {1, 2, 3}?

a. x = 0 and y = 5 c. x = 1 and y = 3

b. x = 1; -1 and y = 5 d. x = -1, 0 and y = 5

28. What is the value of x and y in a given two equal ordered pair below (2x + 1, 3y + 4)

= (-4x - 2, 5 - 2y)?

a. x = -2 ; y = -5 c. x = 2; y = 5

b. x = 1/5; y = 1/2 d. x= -1/2; y = 1/5

29. A group of students were asked whether they like Mathematics, English, or both. If 256 like Mathematics, 184 like English, and 120 like both subjects, how many students were there?

a. 520 c. 320

b. 420 d. 220

a. (2, 2), (2, 6) c. (2, 6), (3, 2), (3, 6)

b. (3, 2), (3, 6) d. (2, 6), (3, 6)