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Sets

Short 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

114 Views

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)'

124 Views

123.

Find the following to make them true statements :

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

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

127 Views

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

122 Views

125.

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

128 Views

126.

If A, B and C be three sets, then

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

122 Views

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?

160 Views

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?

123 Views

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?

125 Views

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?

Set A = set of people who speak English

We have to find n(A)

Set B = set of peoplewho speak Hindi.

Number of people who speak English but not Hindi = n(A-B)

$rightwards double arrow$ $space space space straight n left parenthesis straight A minus straight B right parenthesis space equals space straight n left parenthesis straight A right parenthesis space space minus straight n space left parenthesis straight A intersection straight B right parenthesis$

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Number of people who speak both English and Hindi

$space space space space space space space space space space space equals space straight n left parenthesis straight A intersection straight B right parenthesis space equals space 50$ ....(ii)

from (i) and (ii), we have

n(A) - 50 = 30

$rightwards double arrow$ n(A) = 50+30 = 80

Hence, the number of people who speak English

= n(A) = 80

655 Views