Sets — Telangana (SSC) Class 10 Mathematics Solutions (Free)
Free step-by-step Telangana (SSC) Class 10 Mathematics solutions for "Sets" — important questions with detailed answers, download PDF for board exam preparation.
TL;DR: Free step-by-step Telangana (SSC) Class 10 Mathematics solutions for "Sets" — important questions with detailed answers, download PDF for board exam p…
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Q1: If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}, find A ∪ B and A ∩ B.
Step 1: A ∪ B (union) contains all elements from both sets.
A ∪ B = {1, 2, 3, 4, 5, 6, 7}
Step 2: A ∩ B (intersection) contains only common elements.
A ∩ B = {4, 5}
Final Answer: A ∪ B = {1, 2, 3, 4, 5, 6, 7}, A ∩ B = {4, 5}
Q2: If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 4, 6, 8}, find A'.
Step 1: A' (complement of A) contains all elements of universal set U that are NOT in A.
Step 2: Elements in U but not in A are: 1, 3, 5, 7, 9, 10
Final Answer: A' = {1, 3, 5, 7, 9, 10}
Q3: Prove that (A ∪ B)' = A' ∩ B' using De Morgan's Law.
Step 1: Let x be an arbitrary element.
Step 2: x ∈ (A ∪ B)' means x ∉ (A ∪ B)
Step 3: x ∉ (A ∪ B) means x ∉ A AND x ∉ B
Step 4: This is equivalent to x ∈ A' AND x ∈ B'
Step 5: Therefore x ∈ (A' ∩ B')
Final Answer: (A ∪ B)' = A' ∩ B' (De Morgan's First Law)
Q4: In a Venn diagram, if n(A) = 30, n(B) = 40, n(A ∩ B) = 10, find n(A ∪ B).
Step 1: Use the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
Step 2: n(A ∪ B) = 30 + 40 - 10
Step 3: n(A ∪ B) = 60
Final Answer: n(A ∪ B) = 60
Q5: If A = {x : x is a factor of 12} and B = {x : x is a multiple of 2 and x ≤ 12}, list both sets.
Step 1: Factors of 12 are numbers that divide 12 evenly.
Factors: 1, 2, 3, 4, 6, 12
So A = {1, 2, 3, 4, 6, 12}
Step 2: Multiples of 2 that are ≤ 12 are: 2, 4, 6, 8, 10, 12
So B = {2, 4, 6, 8, 10, 12}
Final Answer: A = {1, 2, 3, 4, 6, 12}, B = {2, 4, 6, 8, 10, 12}
Showing 5 of 8 questions — full solutions on the page.