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: Identify the universal set , set P, and set Q. The universal set consists of counting numbers x such that 1 < x 20. = \2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\ Set P consists of multiples of 3 within . P = \3, 6, 9, 12, 15, 18\ Set Q consists of positive even numbers within . Q = \2, 4, 6, 8, 10, 12, 14, 16, 18, 20\ Step 2: Find the intersection P Q. The intersection P Q contains elements common to both P and Q. P Q = \6, 12, 18\ a) (i) The elements in P Q are \6, 12, 18\. Step 3: List all subsets of P Q. The set P Q has 3 elements. The number of subsets is 2^3 = 8. The subsets are: \6\ \12\ \18\ \6, 12\ \6, 18\ \12, 18\ \6, 12, 18\ a) (ii) The subsets in P Q are \, \6\, \12\, \18\, \6, 12\, \6, 18\, \12, 18\, \6, 12, 18\\. Step 4: Make x the subject of the relation y = 3k - (2)/(x). y = 3k - (2)/(x) Subtract 3k from both sides: y - 3k = -(2)/(x) Multiply both sides by -1: 3k - y = (2)/(x)