Consider three sets X = { 5 , 6 } , Y = { 2 , 3 , 4 } and Z = { n | n ∈ N , n is a prime number less than 10 } . Consider the universal set to be U = { x | x ∈ N , x < 15 } . Which of the following options are correct? Y is a subset of Z Cardinality of ( X ∪ Z ) × ( Z ∪ X ) is 25 Cardinality of ( X ∪ Y ) c ∩ Z is less than the cardinality of X . X ∩ Z c is an empty set
Answers
Answer:
U= N: Set of natural numbers
(i) {x:xis an even natural number}
′
={x:x is an odd natural number}
(ii) {x:xis an odd natural number}
′
={x:xis an even natural number}
(iii) {x:x is a positive multiple of 3}
′
={x:x∈N and x is not a multiple of 3}
(iv) {x:xis a prime number}
′
={x:xis a positive composite number and x=1}
(v) {x:xis a natural number divisible by 3 and 5}
′
={x:xis a natural number that is not divisible by 3 or 5}
(vi) {x:xis a perfect square}
′
={x:x∈Nand x is not a perfect square}
(vii) {x:xis a perfect cube}
′
={x:x∈Nand x is not a perfect cube}
(viii) {x:x+5=8}
′
={x:x∈Nand x
=3}
(ix) {x:2x+5=9}
′
={x:x∈Nandx
=2}
(x) {x:x≥7}
′
={x:x∈Nandx<7}
(xi) {x:xϵNand2x+1>10}
′
={x:x∈Nandx≤
2
9
}
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Solution To Question ID 419644
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SIMILAR QUESTIONS
star-struck
If A={1,2,3,4},U={1,2,3,4,5,6,7,8}, find A
′
in U and draw Venn diagram
Answer:
Consider three sets X = { 5 , 6 } , Y = { 2 , 3 , 4 } and Z = { n | n ∈ N , n is a prime number less than 10 } . Consider the universal set to be U = { x | x ∈ N , x < 15 } .
Y is a subset of Z Cardinality of ( X ∪ Z ) × ( Z ∪ X ) is 25 Cardinality of ( X ∪ Y ) c ∩ Z is less than the cardinality of X