In a survey of 600 students, 150 were found to be drinking tea a

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 Multiple Choice QuestionsShort Answer Type

131. If X and Y are two sets such that (X ∪ Y) has 18 elements, (X ∩ Y) has 5 elements and set Y has 15 elements. How many elements set X have ?
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132.

In a survey of 600 students, 150 were found to be drinking tea and 225 drinking coffee. 100 were drinking both tea and coffee. Find, how many students were neither drinking tea nor coffee?


Let,                 Set A = set of student whio drink tea

   rightwards double arrow                     n(A)  = 150                                                                         ....(i)

                        Set B = set of student who drink coffee                                     .....(ii)

   rightwards double arrow                 n(B)  = 225                       

Number of student drinking both tea and coffee

      space space space space space space space space space space space space space space space space space space space space equals space straight n open parentheses straight A intersection straight B close parentheses space equals space 100                                                                 ...(iii)

Using,       "<pre

  
          space space space space space space space space space space space space space space space space space space space space space space straight n left parenthesis straight A union straight B right parenthesis space equals space 150 space plus 225 space minus 100 space equals space 275 

Total number of studenr of = 600

space space space space space space space space space rightwards double arrow space space space space space space space space space straight n left parenthesis straight U right parenthesis space equals space 600

Hence, the number of students who neither drink tea nor coffee.

      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 equals space straight n space left parenthesis straight A apostrophe intersection straight B apostrophe right parenthesis space equals space straight n left square bracket left parenthesis straight A union straight B right parenthesis apostrophe right square bracket space equals space straight n left parenthesis straight U right parenthesis space minus straight n left parenthesis straight A union straight B right parenthesis

                             = 600 - 275 = 325

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133.  X and Y are two sets such that n (X) = 17, n (Y) = 23, and n (X ∪ Y) = 38, find n (X ∩ Y).
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134.

In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

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135.

If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have?

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136.
Show that A ∩ B = A ∩ C need not imply B = C.
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137.

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C.

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138.

Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B )

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139.

In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

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140.

In a group of 950 residents of a locality, every resident is fond of reading at least one of the morning newspapers published in English and Hindi. 750 of them like to read Hindi newspaper and 460 read the English newspapers. Find how many of them read

(i) Both the English newspaper and the Hindi newspaper.

(ii) English newspaper only.

(iii) Hindi newspaper only.

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