It is known that for any non-empty set A, A x A x A is defined as :
A x A x A = {(a, b, c): a, b, c ∈ A}
It is given that A = {-1, 1}
∴ A x A x A = {(-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (-1, 1, 1), (1, -1, -1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}
If the domain of the function $ f(x) = \log_7(1 - \log_4(x^2 - 9x + 18)) $ is $ (\alpha, \beta) \cup (\gamma, \delta) $, then $ \alpha + \beta + \gamma + \delta $ is equal to
Let $ A = \{-2, -1, 0, 1, 2, 3\} $. Let $ R $ be a relation on $ A $ defined by $ (x, y) \in R $ if and only if $ |x| \le |y| $. Let $ m $ be the number of reflexive elements in $ R $ and $ n $ be the minimum number of elements required to be added in $ R $ to make it reflexive and symmetric relations, respectively. Then $ l + m + n $ is equal to
Let A = $\{-3,-2,-1,0,1,2,3\}$. Let R be a relation on A defined by xRy if and only if $ 0 \le x^2 + 2y \le 4 $. Let $ l $ be the number of elements in R and m be the minimum number of elements required to be added in R to make it a reflexive relation. then $ l + m $ is equal to
take on sth: | to begin to have a particular quality or appearance; to assume sth |
take sb on: | to employ sb; to engage sb to accept sb as one’s opponent in a game, contest or conflict |
take sb/sth on: | to decide to do sth; to allow sth/sb to enter e.g. a bus, plane or ship; to take sth/sb on board |