This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: List the members of set P (factors of 36). The factors of 36 are the numbers that divide 36 evenly. P = \1, 2, 3, 4, 6, 9, 12, 18, 36\ Step 2: List the members of set Q (factors of 54). The factors of 54 are the numbers that divide 54 evenly. Q = \1, 2, 3, 6, 9, 18, 27, 54\ Step 3: Find the intersection of P and Q, denoted as P Q. The intersection consists of elements that are common to both sets P and Q. P Q = \1, 2, 3, 6, 9, 18\ Step 4: Find the number of elements in P Q, denoted as n(P Q). Count the number of elements in the set P Q. n(P Q) = 6 The final answers are: (i) P = \1, 2, 3, 4, 6, 9, 12, 18, 36\ Q = \1, 2, 3, 6, 9, 18, 27, 54\ (ii) P Q = \1, 2, 3, 6, 9, 18\ (iii) n(P Q) = 6 3 done, 2 left today. You're making progress.