Questions: Suppose w, x, y, and z represent the following statements. - w : All cats are white. - x : "Blue" is a letter in the English alphabet. - y : "C" is a letter in the English alphabet. - z: 40-30=10 Which of the following conjunctions are true? Select all that apply: x and y y and z w and y z and x

Suppose w, x, y, and z represent the following statements. - w : All cats are white. - x : "Blue" is a letter in the English alphabet. - y : "C" is a letter in the English alphabet. - z: 40-30=10 Which of the following conjunctions are true? Select all that apply: x and y y and z w and y z and x
Transcript text: Suppose $w, x, y$, and $z$ represent the following statements. - $w$ : All cats are white. - $x$ : "Blue" is a letter in the English alphabet. - $y$ : "C" is a letter in the English alphabet. - $z: 40-30=10$ Which of the following conjunctions are true? Select all that apply: $x \wedge y$ $y \wedge z$ $w \wedge y$ $z \wedge x$
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Solution

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Solution Steps

To determine which conjunctions are true, we need to evaluate the truth value of each individual statement and then apply the logical AND operation (denoted by $\wedge$) to the pairs of statements.

  1. Evaluate the truth value of each statement:

    • $w$: False (Not all cats are white)
    • $x$: False ("Blue" is not a letter in the English alphabet)
    • $y$: True ("C" is a letter in the English alphabet)
    • $z$: True (40 - 30 = 10)

  2. Apply the logical AND operation to each pair of statements:

    • $x \wedge y$: False AND True = False
    • $y \wedge z$: True AND True = True
    • $w \wedge y$: False AND True = False
    • $z \wedge x$: True AND False = False
Step 1: Evaluate the Truth Values of Each Statement

We start by evaluating the truth values of the given statements:

  • \( w \): All cats are white. This is false.
  • \( x \): "Blue" is a letter in the English alphabet. This is false.
  • \( y \): "C" is a letter in the English alphabet. This is true.
  • \( z \): \( 40 - 30 = 10 \). This is true.
Step 2: Apply the Logical AND Operation to Each Pair

Next, we apply the logical AND operation (\( \wedge \)) to each pair of statements:

  • \( x \wedge y \): False AND True = False
  • \( y \wedge z \): True AND True = True
  • \( w \wedge y \): False AND True = False
  • \( z \wedge x \): True AND False = False

Final Answer

\(\boxed{y \wedge z}\)

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