Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 04, 2023

Find the intersection of sets $\mathbf{A}$ and $\mathbf{B}$ given $\mathbf{U}=\{\mathrm{s}, \mathrm{t}, \mathrm{u}, \mathrm{v}, \mathrm{W}, \mathrm{X}, \mathrm{y}, \mathrm{z}\}$ , $\mathbf{A}=\{\mathrm{u}, \mathrm{v}, \mathrm{y}, \mathrm{z}\}$ , and $\mathbf{B}=\{\mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{y}\}$ .

STEP 1

Assumptions1. The universal set U consists of the elements {s, t, u, v, w, x, y, z} . The set A consists of the elements {u, v, y, z}
3. The set B consists of the elements {v, w, x, y}

STEP 2

The intersection of two sets, denoted as A ∩ B, is the set of elements which are in both A and B.
$A \cap B = \{x | x \in A \text{ and } x \in B\}$

STEP 3

Now, we need to find the elements that are common to both sets A and B.

STEP 4

The common elements in sets A and B are {v, y}.
So, the intersection of sets A and B is {v, y}.
$A \cap B = \{v, y\}$ The correct answer is (c) {v, y}.

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