Putting the values into statement 1

• If 2x ≮ 3y & 3x = 4z, then 9y > 8z
• Now checking:
• 2x ≮ 3y can be written as 2x ≥ 3y
• Putting x = 4z/3 into this
• 2 x 4z/3 ≥ 3y
• Or 8z ≥ 9y
• Or 9y ≤ 8z (this is deduction)
• Given 9y > 8z
• Hence, statement 1 is false.

Putting the values into statement 2

• If x < 2y & y ≯ z, then x ≤ z
• Now checking:
• y ≯ z an be written as y ≤ z
• y ≤ z means y + y ≤ z + y or 2y ≤ z + y
• putting it in x < 2y
• x < 2y ≤ z + y
• or x ≤ z + y (this is deduction)
• given x ≤ z
• By comparing the above two equations, we cannot certainly conclude that x ≤ z
• Hence, statement 2 is also wrong.