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.

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.

✓ 100% Free ✓ No Login Needed ✓ NCERT / CBSE Aligned ✓ Download as PDF

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…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated

🤖 Stuck on any question? Ask Syllab's free AI Tutor for a step-by-step explanation — instant, unlimited, no login.

Sets — Textbook Questions Answered (8)

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}

Q6: Show that A - B = A ∩ B' (using Venn diagram logic).

Step 1: A - B consists of elements in A but not in B. Step 2: Elements in A but not in B = elements in A AND elements in B' Step 3: A ∩ B' means the intersection of A with complement of B. Step 4: This gives exactly those elements that belong to A but not to B. Final Answer: A - B = A ∩ B' (Set difference property)

Q7: Three sets have n(A) = 20, n(B) = 15, n(C) = 12, n(A ∩ B) = 7, n(B ∩ C) = 5, n(A ∩ C) = 4, n(A ∩ B ∩ C) = 2. Find n(A ∪ B ∪ C).

Step 1: Use the formula n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C) Step 2: n(A ∪ B ∪ C) = 20 + 15 + 12 - 7 - 5 - 4 + 2 Step 3: n(A ∪ B ∪ C) = 47 - 16 + 2 = 33 Final Answer: n(A ∪ B ∪ C) = 33

Q8: Write the power set of A = {1, 2}.

Step 1: Power set P(A) contains all possible subsets of A. Step 2: Subsets of {1, 2}: - ∅ (empty set) - {1} - {2} - {1, 2} Step 3: A set with n elements has 2ⁿ subsets. Here n = 2, so 2² = 4 subsets. Final Answer: P(A) = {∅, {1}, {2}, {1, 2}}

Related