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Let A : {1, 2, 3, 4, 5, 6, 7}. Define B = {T ⊆ A : either 1 ∉ T or 2 ∈ T} and C = T ⊆ A : T the sum of all the elements of T is a prime number}. Then the number of elements in the set B ∪ C is _______________. (In integers)
Correct answer is '107'. Can you explain this answer?
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Let A : {1, 2, 3, 4, 5, 6, 7}. Define B = {T ⊆ A : either 1 ¬i...
It seems like the rest of your question got cut off. Could you please provide more information about how B is defined?
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Let A : {1, 2, 3, 4, 5, 6, 7}. Define B = {T ⊆ A : either 1 ¬i...
B' is a set containing sub sets of A containing element 1 and not containing 2.
And C' is a set containing subsets of A whose sum of elements is not prime.
So, we need to calculate number of subsets of {3, 4, 5, 6, 7} whose sum of elements plus 1 is composite.
Number of such 5 elements subset = 1
Number of such 4 elements subset = 3 (except selecting 3 or 7)
Number of such 3 elements subset = 6 (except selecting {3, 4, 5}, {3, 6, 7}, {4, 5, 7} or {5, 6, 7})
Number of such 2 elements subset = 7 (except selecting {3, 7}, {4, 6}, {5, 7})
Number of such 1 element subset = 3 (except selecting {4} or {6})
Number of such 0 elements subset = 1
And C' is a set containing subsets of A whose sum of elements is not prime.
So, we need to calculate number of subsets of {3, 4, 5, 6, 7} whose sum of elements plus 1 is composite.
Number of such 5 elements subset = 1
Number of such 4 elements subset = 3 (except selecting 3 or 7)
Number of such 3 elements subset = 6 (except selecting {3, 4, 5}, {3, 6, 7}, {4, 5, 7} or {5, 6, 7})
Number of such 2 elements subset = 7 (except selecting {3, 7}, {4, 6}, {5, 7})
Number of such 1 element subset = 3 (except selecting {4} or {6})
Number of such 0 elements subset = 1
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Let A : {1, 2, 3, 4, 5, 6, 7}. Define B = {T ⊆ A : either 1 ∉ T or 2 ∈ T} and C = T ⊆A : T the sum of all the elements of T is a prime number}. Then the number of elements in the set B ∪ C is _______________. (In integers)Correct answer is '107'. Can you explain this answer?
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Let A : {1, 2, 3, 4, 5, 6, 7}. Define B = {T ⊆ A : either 1 ∉ T or 2 ∈ T} and C = T ⊆A : T the sum of all the elements of T is a prime number}. Then the number of elements in the set B ∪ C is _______________. (In integers)Correct answer is '107'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let A : {1, 2, 3, 4, 5, 6, 7}. Define B = {T ⊆ A : either 1 ∉ T or 2 ∈ T} and C = T ⊆A : T the sum of all the elements of T is a prime number}. Then the number of elements in the set B ∪ C is _______________. (In integers)Correct answer is '107'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A : {1, 2, 3, 4, 5, 6, 7}. Define B = {T ⊆ A : either 1 ∉ T or 2 ∈ T} and C = T ⊆A : T the sum of all the elements of T is a prime number}. Then the number of elements in the set B ∪ C is _______________. (In integers)Correct answer is '107'. Can you explain this answer?.
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