Set Language

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Yes, this is a well-defined set because given any object, we can clearly decide whether it belongs to this set or not. Rule: All even natural numbers between 1 and 11. Each element can be verified to …

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Step 1: Identify all letters in MATHEMATICS: M-A-T-H-E-M-A-T-I-C-S Step 2: List each letter only ONCE (elements listed only once in a set) Step 3: Result = {M, A, T, H, E, I, C, S} Note: Even though …

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Step 1: Identify the pattern - all odd natural numbers from 1 to 15 Step 2: Express the condition using mathematical notation Step 3: Set-builder form = {x : x is an odd natural number and x ≤ 15} OR …

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Step 1: Convert to roster form by finding all factors of 24 Step 2: Start with 24 ÷ 1 = 24, 24 ÷ 2 = 12, 24 ÷ 3 = 8, 24 ÷ 4 = 6 Step 3: All factors: A = {1, 2, 3, 4, 6, 8, 12, 24} Step 4: Count the el…

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Step 1: Substitute values of n ∈ W (whole numbers: 0, 1, 2, 3, ...) n = 0: x = 3(0) + 2 = 2 n = 1: x = 3(1) + 2 = 5 n = 2: x = 3(2) + 2 = 8 n = 3: x = 3(3) + 2 = 11 n = 4: x = 3(4) + 2 = 14 n = 5: x =…

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Step 1: Check if n(A) = n(B) → n(A) = 3, n(B) = 3 ✓ They have same number of elements, so A ≈ B (EQUIVALENT) Step 2: Check if A = B → Does A contain exactly same elements as B? NO 1 ≠ a, 2 ≠ b, 3 ≠ c…

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Step 1: Definition of subset: A is a subset of B if every element of A is also in B Step 2: Check each element of {2, 4}: - Is 2 ∈ {1, 2, 3, 4, 5}? YES ✓ - Is 4 ∈ {1, 2, 3, 4, 5}? YES ✓ Step 3: Since…

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Formula: If n(A) = m, then number of subsets = 2^m Step 1: n(A) = 3 Step 2: Number of subsets = 2³ = 8 Step 3: List them to verify: ∅, {p}, {q}, {r}, {p,q}, {p,r}, {q,r}, {p,q,r} Count: 8 subsets ✓ …