Question

Let \(U\) be the set containing all twelve months in the year, \(A = \{Jan., Feb., Mar., Apr., May, June\}\), and \(B = \{Apr., May, June, July, Aug., Sep., Oct.\}\). Find:

(a) \(A \setminus B\)
(b) \(B \setminus A\)
(c) \(A \cap B\)
(d) \(A \cup B\)

Answer 1

(a) \(A \setminus B = \{\text{Jan., Feb., Mar.}\}\)

(b) \(B \setminus A = \{\text{July, Aug., Sep., Oct.}\}\)

(c) \(A \cap B = \{\text{Apr., May, June}\}\)

(d) \(A \cup B = \{\text{Jan., Feb., Mar., Apr., May, June, July, Aug., Sep., Oct.}\}\)

Explanation:

In set theory, operations like union (\(\cup\)), intersection (\(\cap\)), and set difference (\(\setminus\)) are used to combine or manipulate sets. Let's apply these operations to the given sets:

Given sets:

\[ U = \{\text{Jan., Feb., Mar., Apr., May, June, July, Aug., Sep., Oct., Nov., Dec.}\} \]

\[ A = \{\text{Jan., Feb., Mar., Apr., May, June}\} \]

\[ B = \{\text{Apr., May, June, July, Aug., Sep., Oct.}\} \]

(a) Set difference \(A \setminus B\):

\[ A \setminus B = \{\text{Jan., Feb., Mar.}\} \]

(b) Set difference \(B \setminus A\):

\[ B \setminus A = \{\text{July, Aug., Sep., Oct.}\} \]

(c) Set intersection \(A \cap B\):

\[ A \cap B = \{\text{Apr., May, June}\} \]

(d) Set union \(A \cup B\):

\[ A \cup B = \{\text{Jan., Feb., Mar., Apr., May, June, July, Aug., Sep., Oct.}\} \]

So, the answers are:

(a) \(A \setminus B = \{\text{Jan., Feb., Mar.}\}\)

(b) \(B \setminus A = \{\text{July, Aug., Sep., Oct.}\}\)

(c) \(A \cap B = \{\text{Apr., May, June}\}\)

(d) \(A \cup B = \{\text{Jan., Feb., Mar., Apr., May, June, July, Aug., Sep., Oct.}\}\)