Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Let X and Y be finite sets and f: X -> Y b...
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Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?
- a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|
- b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)
- c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}
- d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)
Correct answer is option 'D'. Can you explain this answer?
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Let X and Y be finite sets and f: X -> Y be a function. Which one o...
Let x = {a, b, c} and y = {1, 2} A Function f maps each element of x to 1 in y. f(a)=1 , f(b)=1 , f(c) =1 A = {a, b} B = {b, c}
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A] |f(A u B) | = |f({a, b, c})| = 3 | f(A)|+|f(B)| = 2 + 2 = 4 , LHS != RHS.
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B] f(A ∩ B) = f({b}) = { 1 } f(A) ∩ f(B) = {1, 1} ∩ {1, 1} = {1, 1} LHS != RHS
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C] |f(A ∩ B)| = |f({b})| = |{ 1 }| = 1 min{|f(A)|,|f(B)|} = min(2,2) = 2 LHS != RHS
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D] In a function a value can be mapped only to one value.
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A] |f(A u B) | = |f({a, b, c})| = 3 | f(A)|+|f(B)| = 2 + 2 = 4 , LHS != RHS.
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B] f(A ∩ B) = f({b}) = { 1 } f(A) ∩ f(B) = {1, 1} ∩ {1, 1} = {1, 1} LHS != RHS
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C] |f(A ∩ B)| = |f({b})| = |{ 1 }| = 1 min{|f(A)|,|f(B)|} = min(2,2) = 2 LHS != RHS
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D] In a function a value can be mapped only to one value.
Most Upvoted Answer
Let X and Y be finite sets and f: X -> Y be a function. Which one o...
Y be a function. The function f is said to be one-to-one (or injective) if for every x1, x2 in X, if f(x1) = f(x2), then x1 = x2. In other words, each element in X maps to a unique element in Y.
The function f is said to be onto (or surjective) if for every y in Y, there exists an x in X such that f(x) = y. In other words, every element in Y is mapped to by at least one element in X.
The function f is said to be bijective if it is both one-to-one and onto. In other words, each element in X maps to a unique element in Y, and every element in Y is mapped to by exactly one element in X.
If a function f is bijective, it means that there is a one-to-one correspondence between the elements of X and Y, and we can say that X and Y have the same cardinality.
The function f is said to be onto (or surjective) if for every y in Y, there exists an x in X such that f(x) = y. In other words, every element in Y is mapped to by at least one element in X.
The function f is said to be bijective if it is both one-to-one and onto. In other words, each element in X maps to a unique element in Y, and every element in Y is mapped to by exactly one element in X.
If a function f is bijective, it means that there is a one-to-one correspondence between the elements of X and Y, and we can say that X and Y have the same cardinality.
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Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer?
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Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer?.
Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer?.
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Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let X and Y be finite sets and f: X -> Y be a function. Which one of the following statements is TRUE?a)For any subsets A and B of X,|f(A∪B)| = |f(A)|+|f(B)|b)For any subsets A and B of X, f(A∩B) = f(A)∩f(B)c)For any subsets A and B of X, |f(A∩B)| =min{|f(A)|,|f(B)|}d)For any subsets S and T of Y, f-1(S∩T) =f-1(s)∩f-1(T)Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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