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91.

Write the following subsets of set R of real numbers in the interval form :

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis straight a right parenthesis space space left curly bracket straight x space colon space straight x space element of space straight R comma space minus 3 space less or equal than space straight c space less or equal than 7 right curly bracket space space space space space space space space left parenthesis straight b right parenthesis space left curly bracket straight x space colon space straight x space element of space straight R comma space minus 23 space less than space straight x space less or equal than space 1 right curly bracket space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis straight c right parenthesis space space left curly bracket straight x space colon space straight x element of straight R comma space 4 less or equal than straight x less than 11 right curly bracket space space space space space space space space space space space space space space space left parenthesis straight d right parenthesis space space left curly bracket straight x space colon space straight x element of space straight R comma space 0 less than straight x less than 5 right curly bracket$

109 Views

92.

Write the following intervals of real numbers in the set-builder form :

(a) [-2, 3] (b) [-1, 4] (c) [5, 27] (d) [2, 11]

98 Views

93.

Write the following subsets of set R of real numbers in the interval form :

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis straight a right parenthesis space space space space left curly bracket straight x space colon space straight x space element of space straight R comma space space straight x space greater or equal than space minus 1 right curly bracket space space space space space space space space space space space space space left parenthesis straight b right parenthesis space space space space left curly bracket straight x space colon space straight x element of space straight R comma space straight X space greater than 0 right curly bracket space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis straight c right parenthesis space space space space space left curly bracket straight x space colon space straight x element of space straight R comma space straight x space less or equal than space 2 right curly bracket space space space space space space space space space space space space space space space space space space left parenthesis straight d right parenthesis space space space space space left curly bracket straight x space colon space straight x space element of space straight R comma space straight x space less than space 3 right curly bracket space$

123 Views

94.

Write the following intervals of real numbers in the set-builder form :

$space space space space space space space space space space space space space space space space space space left parenthesis straight a right parenthesis space space space space space open parentheses negative infinity comma space 2 close parentheses space space space space space space space space space space space space space space space space space left parenthesis straight b right parenthesis space space space space space space space open parentheses negative infinity comma space minus 1 close parentheses space space space space space space space space space space left parenthesis straight c right parenthesis space space left square bracket negative 3 comma space infinity right square bracket$

$space space space space space space space left parenthesis straight d right parenthesis space open parentheses 5 comma space infinity close parentheses$

100 Views

95. A survey was conducted on 800 students of a school with regards to their interest in playing cricket and hockey. 576 of the students said they liked to play circket where as 360 liked to play hockey. What is the least number of students who liked to play both the games ?

118 Views

96.
State whether each of the following statement is true or false. Justify your answer.

(i) {2, 3, 4, 5 } and {3, 6} are disjoint sets. (ii) {a, e, i, o, u} and {a, b, c, d }are disjoint sets. (iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets. (iv) {2, 6, 10} and {3, 7, 11} are disjoint sets

(i) A = {2, 3, 4, 5}, B = {3, 6}

$space space space space rightwards double arrow space space straight A space intersection space straight B space equals space left curly bracket 2 comma space 3 comma space 4 comma space 5 right curly bracket space intersection space left curly bracket 3 comma space 6 right curly bracket space equals space left curly bracket 3 right curly bracket space not equal to straight ϕ$

∴ A and B are not disjoint sets.

(ii) A = {a, e, i, o, u}, B = {a, b, c, d}

$space space space space space space rightwards double arrow space straight A space intersection space straight B space equals space left curly bracket straight a comma space straight e comma space straight i comma space straight o comma space straight u right curly bracket space intersection space left parenthesis straight a comma space straight b comma space straight c comma space straight d right curly bracket space equals space left curly bracket straight a right curly bracket space equals straight ϕ$

∴ A and B are not disjoint sets.

(iii) A = {2, 6, 10, 14}, B = {3, 7, 11, 15}

$space space space space space rightwards double arrow space straight A space intersection space straight B space equals space left curly bracket 2 comma space 6 comma space 10 comma space 14 right curly bracket space intersection space left curly bracket 3 comma space 7 comma space 11 comma space 15 right curly bracket space equals space left curly bracket space right curly bracket space equals space straight ϕ$

Hence, A and B are not disjoint sets.

(iv) A = {2, 6, 10}, B = {3, 7, 11}

$space space space space space space space rightwards double arrow space space straight A space intersection space straight B space equals space left curly bracket 2 comma space 6 comma space 10 right curly bracket space intersection space left curly bracket 3 comma space 7 comma space 11 right curly bracket$

Hence, A and B are not disjoint sets.