If p = (y : 2y \(\geq\) 6) and Q = (y : y -3 \(\geq\) 4), where y is an integer, find p\(\cap\)Q

The set p represents all values of y such that 2y is greater than or equal to 6. Simplifying the inequality 2y \(\geq\) 6 gives y \(\geq\) 3. Therefore, p can be written as p = {y: y \(\geq\) 3}. Similarly, the set Q represents all values of y such that y - 3 is greater than or equal to 4. Simplifying the inequality y - 3 \(\geq\) 4 gives y \(\geq\) 7. Therefore, Q can be written as Q = {y: y \(\geq\) 7}. The intersection of p and Q, denoted by p\(\cap\)Q, is the set of all values of y that are in both p and Q. Since p contains all values of y greater than or equal to 3 and Q contains all values of y greater than or equal to 7, the intersection of p and Q is {y: y \(\geq\) 7}. Therefore, p\(\cap\)Q = {7, 8, 9, 10, ...}. The correct option is (c) {3, 4, 5, 6, 7}.