Sets and Their Types β€” Types of Sets

Topic: Sets and Their Types
πŸ“Œ Example 1. Identify which of the following set is an empty set, singleton set, infinite set or equal sets.
(i) A={x∢x is a girl being living on the Jupiter}
(ii) B={x∢x is a letter in the word ”MARS”}
(iii) C={y∢y is a letter in the word ”ARMS’”}
(iv) D={x∢3x-2=0, xβˆˆβ„š}
(v) E={x∢xβˆˆβ„• and x is an odd number}
✍ Solution:
(i) A={x∢x is a girl being living on the Jupiter}.
We know that, there is no human being or any girl being living on the Jupiter. Hence, A is an empty set.
(ii) B={x∢x is a letter in the word β€œMARS”}
β‡’ B={M, A, R, S}
(iii) C={y∢y is a letter in the word β€œARMS”}
β‡’ C={A, R, M, S}
Here, we observe that the elements of sets B and C are exactly same, hence these sets are equal.
(iv) D={x: 3x-2=0, xβˆˆβ„š}
β‡’ D={β…”}

[∡3x-2=0β‡’x=β…”βˆˆβ„š]

Hence, D is a singleton set.
(v) E={x∢xβˆˆβ„• and x is an odd number}.
Clearly, it is an infinite set because there are infinite natural numbers which are odd.

Types of Sets
πŸ“Œ Example 2. From the sets given below, select empty set, singleton set, infinite set and equal sets.
(i) A={x∢x<1 and x>3}
(ii) B={x∢x3-1=0,xβˆˆβ„}
(iii) C={x∢xβˆˆβ„• and x is a prime number}
(iv) D={2, 4, 6, 8, 10}
(v) E={x∢x is positive even integer and x≀10}
✍ Answers:
(i) Empty set (ii) Singleton set (iii) Infinite set (iv) and (v) Equal sets

πŸ“Œ Example 3. Let A={letters of BOMBAY} and B={letters of CALCUTTA}
(i) Are these sets disjoint or overlapping?
(ii) Are these sets equal?
(iii) Are these sets equivalent?
(iv) Is any of these sets, subset of the other?
(v) Describe a universal set for this problem.
✍
A={letters of BOMBAY}={A, B, M, O, Y}
B={letters of CALCUTTA}={A, C, L, T, U}.
Answers:
(i) These sets are overlapping.
(ii) These sets are not equal.
(iii) These sets are equivalent.
(iv) Neither AβŠ†B nor BβŠ†A.
(v) {Letters of English alphabet}.

πŸ‘‘ Particular Symbols β„• π•Ž β„€ β„š 𝕋 ℝ β„‚ Represent Number Sets in Mathematics πŸ’Ž

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