Explanation:

Correct option 4: Neither 1 not 2

Statement 1: “If 2x is not less than 3y AND 3x equals 4z, then 9y is greater than 8z”

Analysis:
1. From 3x equals 4z, we can say x equals 4z/3
2. Putting this in first condition: 2(4z/3) is not less than 3y
3. Simplifying: 8z/3 is not less than 3y
4. Multiplying both sides by 3: 8z is not less than 9y
5. Therefore: 9y is less than or equal to 8z
6. But statement claims 9y is greater than 8z
7. This is a contradiction

Statement 2: “If x is less than 2y AND y is not greater than z, then x is not greater than z”

Analysis:
1. From first condition: x < 2y
2. From second condition: y ≤ z
3. Putting these together: x < 2z
4. However, x < 2z does not guarantee that x ≤ z
5. Counter example: Let z = 1, y = 1, x = 1.9
– Here x < 2y is true (1.9 < 2)
– y ≤ z is true (1 ≤ 1)
– But x ≤ z is false (1.9 is not ≤ 1)

Therefore, both statements are false.