Question
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निर्देश: निम्नलिखित वेंन आरेख पर विचार कीजिए, जहाँ X, Y और Z तीन समुच्चय हैं। मान लीजिए Z में तत्वों की संख्या को n(Z) द्वारा दर्शाया गया है जो 90 के बराबर है।
n(X) + n(Y) + n(Z) - n(X ∩ Y) - n(Y ∩ Z) - n(X ∩ Z) + n(X ∩ Y ∩ Z) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
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दिया गया है: n(Z) = 90,
उपरोक्त आरेख से, हमें निम्न प्राप्त होता है
n(X) = a + 46, n(Y) = b + 51, n(X ∩ Y) = 16 + 18 = 34, n(Y ∩ Z) = 17 + 18 =35, n(X ∩ Z) = 12 + 18 = 30, n(X ∩ Y ∩ Z) = 18
n(X) + n(Y) + n(Z) - n(X ∩ Y) - n(Y ∩ Z) - n(X ∩ Z) + n(X ∩ Y ∩ Z) =
a + 46 + b + 51 + 90 - 34 - 35 - 30 + 18
= a + b + 106
अतः विकल्प (4) सही है।
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