Page 23 - Algebra 1

Exercise
1. The relation R of Set P of all the textbooks owned by Sam is defined by R = {(𝑝, 𝑞): 𝑝 𝑎𝑛𝑑 𝑞 h𝑎𝑣𝑒 𝑡h𝑒 𝑒𝑞𝑢𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑝𝑎𝑔𝑒𝑠}. Find the type of relation.
a) Only reflexive b) Only transitive c) Only symmetric d) Equivalence
e) Both reflexive and transitive
2. The relation R of Set P of real number R = {(𝑝, 𝑞): 𝑝 ≤ 𝑞4}. Find the type of relation.
a) Only reflexive b) Only transitive c) Only symmetric d) Equivalence
e) None of the above
3. Which of the following are relations from Q to P where P = {1, 2} and Q = {𝑝, 𝑞, 𝑟}.
(i) (p, 1), (p, 2)
(iii) (1, p), (2, p), (1, r)
a) Only (i)
c) (i), (ii), (iv) e) (i) and (iii)
(ii) (q, 1), (r, 2) (iv)(r, 1), (q, 2)
b) (ii), (iii) d) Only (iv)
4. The relation R in the set {3, 4, 5, 6}, given by R = {(3, 4), (4, 3)} is which type of relation?
a) Only reflexive b) Only symmetric c) Only transitive d) Equivalence
e) None of the above
5. Ifn(P)=6andn(Q)=3,thenwhatwouldbethenumberofrelationsofP×Q?
a) 218
c) 28 e) 23
Answers
1. d 2. e 3. c 4. b 5. a
b) 212 d) 220
Page 22 of 54
ALGEBRA