In a committee, 50 people speak French, 20 speak Spanish and 10

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 Multiple Choice QuestionsShort Answer Type

121. Show that :

space space space space space space space straight A union left parenthesis straight B minus straight A right parenthesis space equals space straight A union straight B

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122.

If U = {a, b, c, d, e, f, g, h, k}, A = {a, b, c, d), B  = {b, d, f, h}, C = {c, d, e, f} find 

(a) B'     (b)   C'        space space space space space space space space space space space space left parenthesis straight c right parenthesis space space space left parenthesis straight A union straight B right parenthesis apostrophe space space space space space space space space space space space space space left parenthesis straight d right parenthesis space open parentheses straight B union straight C close parentheses apostrophe space space space space space space space space  (e)   (B - C)'
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123.

Find the following to make them true statements :


space space space space space space space space space left parenthesis straight a right parenthesis space space left parenthesis straight ϕ apostrophe right parenthesis apostrophe intersection straight A space equals space...... space space left parenthesis straight b right parenthesis space left parenthesis straight U apostrophe right parenthesis apostrophe union straight A space equals space....... space space space space space left parenthesis straight c right parenthesis space left parenthesis straight A intersection straight B right parenthesis apostrophe space equals space.......

space space space space space space space space space space space left parenthesis straight d right parenthesis space open parentheses straight A intersection straight ϕ close parentheses apostrophe space equals space....... space space space space space space left parenthesis straight e right parenthesis space open parentheses straight A union straight A apostrophe close parentheses apostrophe equals space......... space space space space space left parenthesis straight f right parenthesis space open parentheses straight A intersection straight A apostrophe close parentheses apostrophe space equals space.......... space space space space space space space

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124. If A and B are two sets, then

space space space space space space left parenthesis straight i right parenthesis space straight n left parenthesis straight A minus straight B right parenthesis space equals space straight n left parenthesis straight a right parenthesis minus straight n left parenthesis straight A intersection straight B right parenthesis          
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125.

Prove that :  space space space space space straight n left parenthesis straight A increment straight B right parenthesis space equals straight n left parenthesis straight A right parenthesis space plus space straight n left parenthesis straight B right parenthesis minus 2 straight n space left parenthesis straight A intersection straight B right parenthesis

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126.

If A, B and C be three sets, then

space space space space space space space space space space space space space space space straight n left parenthesis straight A union straight B union straight V right parenthesis space equals space straight n left parenthesis straight A right parenthesis space plus straight n left parenthesis straight B right parenthesis space plus straight n left parenthesis straight C right parenthesis space minus straight n left parenthesis straight A intersection straight B right parenthesis minus straight n left parenthesis straight B intersection straight C right parenthesis minus straight n left parenthesis straight C intersection straight A right parenthesis plus straight n left parenthesis straight A intersection straight B intersection straight C right parenthesis

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127.

In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

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128.  X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and (X ∩ Y) has 10 elements. How many elements does Y have?
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129.

In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?


Let A = set of people who can speak  French.

rightwards double arrow n(A)  = 50                  
                                                                                                                               ....(i)
B = set of people who speak Spanish


rightwards double arrow space n(B)  = 20                                                                                                         ....(ii)

Number of people who speak both languages = space space space space space straight n left parenthesis straight A intersection straight B right parenthesis space equals space 10                                ....(iii)

Number of people who speak at least one of the two languages space space space space space space space space space equals straight n left parenthesis straight A intersection straight B right parenthesis            ....(iv)

We know that 

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 straight n left parenthesis straight A right parenthesis space plus straight n left parenthesis straight B right parenthesis space minus straight n left parenthesis straight A intersection straight B right parenthesis

∴     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 50 space plus 20 space minus 10 space equals space 60

 Hence, the number of people who speak at least one of the two languages

space space space space space space space space space space space space space space equals space straight n left parenthesis straight A union straight B right parenthesis space equals 60





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130. In a group of people, 50 speak both English and Hindi and 30 speak English but not Hindi. If all the people speak at least one of the two languages, how many speak English?
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