Match List-I with List-II List I List II A. ϕ ∩ {ϕ} I. ϕ B. {ϕ} ∩ {ϕ} II. {ϕ}…
2023
Match List-I with List-II
List I | List II |
|---|---|
A. ϕ ∩ {ϕ} | I. ϕ |
B. {ϕ} ∩ {ϕ} | II. {ϕ} |
C. {ϕ, {ϕ}} − ϕ | III. {{ϕ}} |
D. ϕ ∪ {{ϕ}} | IV. {ϕ, {ϕ}} |
Choose the correct answer from the options given below:
Answer: D. (A)-(I),(B)-(II),(C)-(IV),(D)-(III) — Solution: Compute ∅ ∩ {∅} = ∅. The empty set has no elements, so there is no element common to both sets. Compute {∅} ∩ {∅} = {∅}. The intersection of a set…
- A.
(A)-(I),(B)-(II),(C)-(III),(D)-(IV)
- B.
(A)-(II),(B)-(I),(C)-(III),(D)-(IV)
- C.
(A)-(II),(B)-(I),(C)-(IV),(D)-(III)
- D.
(A)-(I),(B)-(II),(C)-(IV),(D)-(III)
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Correct answer: D
Solution:
Compute ∅ ∩ {∅} = ∅. The empty set has no elements, so there is no element common to both sets.
Compute {∅} ∩ {∅} = {∅}. The intersection of a set with itself is the same set.
Compute {∅, {∅}} − ∅ = {∅, {∅}}. Subtracting the empty set removes nothing, so the original set remains unchanged.
Compute ∅ ∪ {{∅}} = {{∅}}. The union with the empty set yields the other set unchanged.
Therefore the correct pairings are:
∅ ∩ {∅} matches ∅.
{∅} ∩ {∅} matches {∅}.
{∅, {∅}} − ∅ matches {∅, {∅}}.
∅ ∪ {{∅}} matches {{∅}}.
In other words: ∅ ∩ {∅} → ∅; {∅} ∩ {∅} → {∅}; {∅, {∅}} − ∅ → {∅, {∅}}; ∅ ∪ {{∅}} → {{∅}}. The choice that lists these four mappings is the correct answer.