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

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

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.

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