Write 4 set builder notation for

Q={4, 6, 9, 10,12, 14,}

To write set builder notation for the set Q={4, 6, 9, 10, 12, 14}, we need to express the set in terms of its properties or characteristics.

1. Q = {x | x is an element of Q and x is even}:
This set builder notation represents the set Q, where each element 'x' belongs to Q and is an even number. Therefore, Q = {x | x is even and x ∈ {4, 6, 9, 10, 12, 14}}.

2. Q = {x | x is an element of Q and x is a multiple of 3}:
This notation specifies that each element 'x' belongs to Q and is a multiple of 3. Hence, Q = {x | x is a multiple of 3 and x ∈ {4, 6, 9, 10, 12, 14}}.

3. Q = {x | x is an element of Q and x is greater than 8}:
Here, the set builder notation states that each element 'x' belongs to Q and is greater than 8. So, Q = {x | x > 8 and x ∈ {4, 6, 9, 10, 12, 14}}.

4. Q = {x | x is an element of Q and x is not a prime number}:
In this case, the set builder notation indicates that each element 'x' belongs to Q and is not a prime number. Thus, Q = {x | x is not prime and x ∈ {4, 6, 9, 10, 12, 14}}.

These are four possible set builder notations for the set Q={4, 6, 9, 10, 12, 14}. You can modify these notations based on different characteristics or properties you want to emphasize.