Short Answer TypeWe know that a matrix of order m x n has mnelements. Therefore, for finding all possible orders of a matrix with 18 elements, we will find all ordered pairs with products of elements as 18
∴ all possible ordered pairs areall possible ordered pairs areall possible ordered pairs areall possible ordered pairs areall possible ordered pairs areall possible ordered pairs are
(I, 18). (18, 1). (2, 9). (9. 2). (3, 6). (0, 3)
∴ possible orders are 1 x 18. 18 x 1. 2 x 9,-9 X 2, 3 x 6. 6 x 3.
If number of elements = 5, then possible orders arc 1 x 5. 5 x I.
Give an example of a relation which is
(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.
Long Answer TypeDetermine whether each of the following relations are reflexive, symmetric and transitive :
(i) Relation R in the set A = {1, 2, 3,....., 13, 14} defined as
R = {(x, y) : 3 x – y = 0}
(ii) Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x < 4} (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x,y) : y is divisible by x} (iv) Relation R in the set Z of all integers defined as R = {(x,y) : x – y is an integer}
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y) : x and y work at the same place}
(b) R = {(x,y) : x and y live in the same locality}
(c) R = {(x, y) : x is exactly 7 cm taller than y}
(d) R = {(x, y) : x is wife of y}
(e) R = {(x,y) : x is father of y}
Short Answer Type
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