1Given \( A = \{2, 4, 6, 8, 10, 12\} \), \( B = \{1, 3, 5, 7, 9, 11\} \), \( C = \{0, 1, 3, 5, 7, 11\} \), \( D = \{5, 6, 7, 8, 10\} \) and \( E = \{0, 2, 9, 12\} \), say whether each pair is overlapping or disjoint: (a) A and B (b) A and C (c) B and C (d) A and D (e) A and E.
2Given \( U = \{a, b, c, d, e, f, g, h, i, j\} \), \( P = \{a, b, c, d, e, i\} \), \( Q = \{a, e, i\} \), \( R = \{b, c, d, j\} \), \( S = \{i, e, a\} \) and \( T = \{a, b, c, f\} \), state the relation for (a) P and Q (b) Q and R (c) Q and S (d) R and T.
3If \( A = \{0, 1, 2, 3, 4, 5\} \), write these sets by listing: (a) the set B formed by adding 1 to each member of A (b) the set C formed by multiplying each member of A by 2 (c) the set D of the odd numbers in A (d) the set E of the factors of 10 that are in A (e) a universal set U that covers all of them.
4If \( M = \{x : x \text{ is a multiple of } 5 \text{ up to } 40\} \), write by listing (a) the set N formed by adding 3 to each member of M (b) the set P formed by multiplying each member of M by 2 (c) the set Q of the odd numbers in M (d) the set R of the multiples of 10 in M, and then state how each relates to M.
5If \( N = \{x : x \text{ is a counting number up to } 5\} \), write N by listing and say how many subsets it has in all.
6Write and name every subset that can be built from (a) \( F = \{\text{mango}\} \) (b) \( V = \{\text{radish, pumpkin}\} \) (c) \( T = \{\text{bus, jeep, ship}\} \).
7If \( P = \{2, 3, 5\} \), build every subset of P and separate the proper subsets from the improper one.
8A and B are subsets of a universal set U, with \( A = \{2, 4, 6\} \) and \( B = \{1, 2, 3\} \). (a) What kind of sets are A and B, and why? (b) Write the improper subset of A. (c) Which proper subsets do A and B have in common?
9Given \( A = \{3, 5\} \) and \( B = \{2, 4, 7\} \): (a) build all the proper subsets of A (b) which member should be added to A to make A and B overlapping, and why?
10Q and R are subsets of \( U = \{1, 2, 3, 4, 5\} \), with \( Q = \{1, 3, 5\} \) and \( R = \{1, 2, 3\} \). (a) Write the proper and the improper subsets of Q. (b) Which proper subsets do R and Q share? (c) What is the relation between R and Q?
11Given \( M = \{a, b, c\} \) and \( N = \{b, d, f\} \): (a) write the proper and improper subsets of each (b) are the numbers of proper subsets equal? (c) which member removed from M would make M and N disjoint?
12\( A = \{0, 2\} \), \( B = \{1, 2\} \) and \( C = \{\text{square numbers from } 2 \text{ to } 5\} \) are subsets of a universal set U. (a) Write the proper and improper subsets of C. (b) What kind of sets are A and B? (c) Which of A and C has more subsets, and why?
13Why can a set never be a proper subset of itself?
14How many proper subsets can be built from a set with 12 members?
15Choose two domestic animals found in your community, build two sets from their features, and say with a reason whether those sets are disjoint or overlapping.