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: Define the universal set U. The universal set U = \x 18 x 36\ includes all integers from 18 to 36, inclusive. U = \18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36\ Step 2: List the elements of set P. Set P consists of multiples of 3 within U. P = \18, 21, 24, 27, 30, 33, 36\ a.i) P = \18, 21, 24, 27, 30, 33, 36\ Step 3: List the elements of set Q. Set Q consists of factors of 72 within U. The factors of 72 are \1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72\. Q = \18, 24, 36\ a.ii) Q = \18, 24, 36\ Step 4: List the elements of set R. Set R consists of even numbers within U. R = \18, 20, 22, 24, 26, 28, 30, 32, 34, 36\ a.iii) R = \18, 20, 22, 24, 26, 28, 30, 32, 34, 36\ Step 5: List the elements of P Q. P Q represents the intersection of sets P and Q, containing elements common to both sets. P Q = \18, 24, 36\ a.iv) P Q = \18, 24, 36\ Step 6: List the elements of P' R. First, find P', the complement of P. P' contains all elements in U that are not in P. P' = U - P = \19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35\ Next, find P' R, the intersection of P' and R. P' R = \20, 22, 26, 28, 32, 34\ a.v) P' R = \20, 22, 26, 28, 32, 34\