Given the following boolean variable values: x = true, y = true, z = false. Determine whether each expression is true (T) or false (F): 1) !(y || z) || x 2) z && x && y 3) !y || (z || x) 4) x || (x && z)

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Given the boolean variable values:

x=true,y=true,z=false

Let's evaluate each expression:

  • ¬(y∣∣z)∣∣x

¬(y∣∣z)=¬(true∣∣false)=¬(true)=false

false∣∣x=false∣∣true=true

Answer: true

  • z&&x&&y

z&&x&&y=false&&true&&true=false

Answer: false

  • ¬y∣∣(z∣∣x)

¬y=¬true=false

z∣∣x=false∣∣true=true

false ∣∣ true=true

Answer: true

  • x∣∣(x&&z)

x=true

x&&z=true&&false=false

x∣∣(x&&z)=true∣∣false=true

Answer: true

Therefore:

  1. ¬(y∣∣z)∣∣x is true
  2. z&&x&&y is false
  3. ¬y∣∣(z∣∣x) is true
  4. x∣∣(x&&z) is true

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