We read your photo as:

If A = 1, 2, 3, 4 and B = 3, 5, 6, find (a) A∩B (b) AUB (c) (A∩B)UB (d) (AUB)NA

Mathematics

ScanSolve AI Answer

Answers

4 parts
a

A∩B={3}A \cap B = \{3\}

b

A∪B={1,2,3,4,5,6}A \cup B = \{1, 2, 3, 4, 5, 6\}

c

(A∩B)∪B={3,5,6}(A \cap B) \cup B = \{3, 5, 6\}

d

(A∪B)∩A={1,2,3,4}(A \cup B) \cap A = \{1, 2, 3, 4\}

Step-by-step solution

6 steps

Given the sets:
A={1,2,3,4}A = \{1, 2, 3, 4\}
B={3,5,6}B = \{3, 5, 6\}

Part a· 1 step

Find A∩BA \cap B.

  1. Identify the elements common to both set A and set B.

    A∩B={x∣x∈A and x∈B}A \cap B = \{x \mid x \in A \text{ and } x \in B\}

    The only element present in both sets A and B is 3.

    A∩B={3}\boxed{A \cap B = \{3\}}

Part b

A∪B={1,2,3,4,5,6}A \cup B = \{1, 2, 3, 4, 5, 6\}

Find A∪BA \cup B.

  1. Combine all unique elements from set A and set B.

    A∪B={x∣x∈A or x∈B}A \cup B = \{x \mid x \in A \text{ or } x \in B\}

    List all elements from A, then add any elements from B that are not already in the list.

    A∪B={1,2,3,4,5,6}A \cup B = \{1, 2, 3, 4, 5, 6\} A∪B={1,2,3,4,5,6}\boxed{A \cup B = \{1, 2, 3, 4, 5, 6\}}

Part c

(A∩B)∪B={3,5,6}(A \cap B) \cup B = \{3, 5, 6\}

Find (A∩B)∪B(A \cap B) \cup B.

  1. First, find A∩BA \cap B.

    From part (a), we know A∩B={3}A \cap B = \{3\}.

  2. Now, find the union of {3}\{3\} with set B.

    {3}∪B={3}∪{3,5,6}\{3\} \cup B = \{3\} \cup \{3, 5, 6\}

    Combine all unique elements.

    {3}∪{3,5,6}={3,5,6}\{3\} \cup \{3, 5, 6\} = \{3, 5, 6\} (A∩B)∪B={3,5,6}\boxed{(A \cap B) \cup B = \{3, 5, 6\}}

Part d

(A∪B)∩A={1,2,3,4}(A \cup B) \cap A = \{1, 2, 3, 4\}

Find (A∪B)∩A(A \cup B) \cap A.

  1. First, find A∪BA \cup B.

    From part (b), we know A∪B={1,2,3,4,5,6}A \cup B = \{1, 2, 3, 4, 5, 6\}.

  2. Now, find the intersection of {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\} with set A.

    {1,2,3,4,5,6}∩A={1,2,3,4,5,6}∩{1,2,3,4}\{1, 2, 3, 4, 5, 6\} \cap A = \{1, 2, 3, 4, 5, 6\} \cap \{1, 2, 3, 4\}

    Identify the elements common to both sets.

    {1,2,3,4,5,6}∩{1,2,3,4}={1,2,3,4}\{1, 2, 3, 4, 5, 6\} \cap \{1, 2, 3, 4\} = \{1, 2, 3, 4\} (A∪B)∩A={1,2,3,4}\boxed{(A \cup B) \cap A = \{1, 2, 3, 4\}}
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QGiven the sets A, B and ξ defined as A=1,2,5,7, B=2,3,6,7, ξ=1,2,3,4,5,6,7,8,9,10. Find (a) A', (b)…QIf A⁻¹ = [[1, 2], [3, 4]] and B⁻¹ = [[−2, 4], [6, 8]], find (a) (A^T)⁻¹, (b) (AB)⁻¹, (c) (2B)⁻¹. If…QGiven sets A = 2, 3, 5, 7, B = 2, 3, 4, 5, 6, 7, 8, 9, and C = 1, 4, 9, 16, 25, 36, find (A ∪ B) ∩ C…QA = (1 2 / 0 1) B = (3 1 / 2 0) find 2A + B. C = (2 −3 / 0 4) and D = (5 −2 / −7 1) Express as a…QletA=[2,(a,4),7]andB=[3,4,(a)]thanfindAuB,AnB
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp