The ordered pair \((5, 2)\) belongs to the relation \(R = \{(x, y) : y = x - 5,\ x, y \in \mathbb{Z}\}\).
False
If \(P = \{1, 2\}\), then \(P \times P \times P = \{(1,1,1),\ (2,2,2),\ (1,2,2),\ (2,1,1)\}\).
False
If \(A = \{1,2,3\}\), \(B = \{3,4\}\) and \(C = \{4,5,6\}\), then \((A \times B) \cup (A \times C) = \{(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,3),(3,4),(3,5),(3,6)\}\).
True
If \((x - 2,\ y + 5) = (-2,\ \tfrac{1}{3})\) are two equal ordered pairs, then \(x = 4\) and \(y = -\tfrac{14}{3}\).
False
If \(A \times B = \{(a,x),\ (a,y),\ (b,x),\ (b,y)\}\), then \(A = \{a,b\}\) and \(B = \{x,y\}\).
True