This solution covers multiple math problems involving sets, including listing elements, set-builder notation, and identifying equivalent sets.

You're on a roll — here are the solutions to the math problems. Question (e) from the first image: Which is the set of prime numbers less than 10? The prime numbers less than 10 are 2, 3, 5, and 7. (1 is not a prime number). The correct option is ii. \2, 3, 5, 7\. 4. A is the set of natural numbers between 0 and 10 exclusive. a) List the elements of the set A. Natural numbers start from 1. "Between 0 and 10 exclusive" means numbers greater than 0 and less than 10. A = \1, 2, 3, 4, 5, 6, 7, 8, 9\ b) Use or if 2, 3, 0, 9, 11 belong or do not belong to the set A. 2 A 3 A 0 A 9 A 11 A c) Write the set in set-builder notation. A = \x x N, 0 < x < 10\ 5. a) List the members of the following sets. A = odd numbers from 0 to 10 A = \1, 3, 5, 7, 9\ B = prime numbers between 10 and 24 B = \11, 13, 17, 19, 23\ C = multiples of 7 between 6 and 50 C = \7, 14, 21, 28, 35, 42, 49\ b) Which sets are equivalent among A, B and C? Equivalent sets have the same number of elements. Number of elements in A, |A| = 5. Number of elements in B, |B| = 5. Number of elements in C, |C| = 7. Sets A and B have the same number of elements. The equivalent sets are A and B. 6. Given that P = \0, 1, 3, 5\, Q = \5, 3, 1\, R = \0\, S = \1\, T = and S = \3, 1, 5\. Assumption: The second definition of S, S = \3, 1, 5\, overwrites the first definition S = \1\. So, the sets are: P = \0, 1, 3, 5\, Q = \5, 3, 1\, R = \0\, S = \3, 1, 5\, T = . a) Write down the number of elements in each set. |P| = 4 |Q| = 3 |R| = 1 |S| = 3 |T| = 0 b) Which of the sets are equal? Equal sets contain exactly the same elements. Q = \5, 3, 1\ and S = \3, 1, 5\ contain the same elements. The equal sets are Q and S. c) Which of the sets have equal number of elements but the sets are not equal? From part (a), |Q|=3 and |S|=3. However, Q and S are equal sets. There are no other pairs of sets with an equal number of elements that are not themselves equal. None 7. a) If A = \a, b, c, d\ and B = \a, b, c, d, e\, all elements of A are also the elements of B, but again A ≠ B. Why? A ≠ B because set B contains an element 'e' that is not present in set A. For two sets to be equal, they must contain exactly the same elements. b) If P = \g, o, d\ and Q = \c, u, p\, why are P and Q not equal sets? But P is equivalent to Q. Why? P and Q are not equal sets because they do not contain the same elements (e.g., 'g' is in P but not in Q). They are equivalent sets because they have the same number of elements: |P|=3 and |Q|=3. 8. A = \1, 2, 3, 4, 5\ is a given set. Write the following subsets of A (i) by listing (ii) by set-builder notation. a) B = Set of elements of A that are prime numbers (i) B = \2, 3, 5\ (ii) B = \x x A and x is a prime number\ b) C = Set of elements of A that are even numbers (i) C = \2, 4\ (ii) C = \x x A and x is an even number\ c) D = Set of elements of A that are odd numbers (i) D = \1, 3, 5\ (ii) D = \x x A and x is an odd number\ d) E = Set of elements of A that are even prime numbers (i) E = \2\ (ii) E = \x x A and x is an even prime number\ e) F = Set of elements of A that are between 1 and 4 (i) F = \2, 3\ (ii) $F = \x x A and 1 <