What is [math: T∩A]?

Question

BlackTom AI · Accepted Answer

The intersection of two sets contains exactly those elements that appear in both sets. Here the elements common to T and A are 3 and 6, so T ∩ A = {3, 6}.

1) Relevant knowledge points and concepts
- Definition: A ∩ B = {x : x ∈ A and x ∈ B}.  
- When computing an intersection you test each element to see whether it belongs to both sets.  
- Notational nuance: {{...}} denotes a set whose single element is itself a set (a different object than {...}).

2) Step‑by‑step reasoning
- List the elements of T and A (as given in the problem context or diagram).  
- Examine each element that appears in either set and ask: is this element in both T and A?  
- Elements that are in both are kept; elements found in only one set are discarded.

3) Intermediate checking (element-by-element)
- Check 3: 3 appears in T and also in A → include 3.  
- Check 6: 6 appears in T and also in A → include 6.  
- Check 4 and 5: each of these appears in only one of the sets (not in both) → exclude them.  
- No other elements are in both sets.

4) Why the correct answer is correct
- By the definition of intersection, only elements present in both sets remain. After checking, only 3 and 6 satisfy that condition, so T ∩ A = {3, 6}.

5) Why the other options are incorrect
- "{{3, 4, 5, 6}}" is a set whose single element is the set {3,4,5,6} (wrong object and includes elements not common).  
- "{3, 4, 5, 6}" lists 4 and 5 as part of the intersection, but 4 and 5 are not in both sets, so this is incorrect.  
- "{{3, 6}}" is a set whose single element is the set {3,6} (different object from {3,6}).  
- "T" is incorrect unless T happens to equal A; the intersection is typically a subset of T, not the entire T, so selecting T is incorrect here.

6) Conclusion
- Therefore T ∩ A = {3, 6}, which matches the provided correct answer {3,6}.

What is [math: T∩A]?Single choice

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