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Question
STRETCH YOUR MIND!
1. If x and y are sets such that x has 2 more elements than y and 96 more subsets that y, how many elements are in x?
Answer #1 for Questions: STRETCH YOUR MIND!
1. If x and y are sets such that x has 2 more elements than y and 96 more subsets that y, how many elements are in x?
Answer:
7
Step-by-step explanation:
Required Answer:
Number of elements in set x.
Formula:
N(⊂ₓ) = 2ᵃ, where a is the number of elements of set x.
Equations:
Let the number of elements in sets x and y be a and b respectively.
So that we have 2 equations:
(1) a = b + 2
(2) 2ᵃ = 2ᵇ + 96
Solution:
From (2), 2ᵃ = 2ᵇ + 96 ⇔ 2ᵃ – 2ᵇ = 96
From (1), 2ᵃ – 2ᵇ = 96 ⇔ 2ᵇ⁺² – 2ᵇ = 96
So
2ᵇ⁺² – 2ᵇ = 96
=> (2ᵇ · 2²) – 2ᵇ = 96
=> 2ᵇ(2² – 1) = 96
=> 2ᵇ · 3 = 96
=> 2ᵇ = 32
=> log₂(2ᵇ) = log₂(32)
=> b = log₂(2⁵)
=> b = 5
∴ a = 5 + 2 = 7
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