0 votes 0 votes Find a common domain for the variables x, y, and z for which the statement ∀x∀y((x = y) → ∀z((z = x) ∨ (z = y))) is true and another domain for which it is false. Mathematical Logic discrete-mathematics propositional-logic engineering-mathematics kenneth-rosen + – ykrishnay asked Apr 18, 2022 ykrishnay 253 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply shishir__roy commented Apr 19, 2022 reply Follow Share Given statement is True when x, y, z $\in$ {1} and is False when x, y, z $\in$ {1, 2}; counter example (1=1) $\implies$ ( (2=1) $\lor$ (2=1) ) is False ie statement is False when x = y = 1 and z = 2. 1 votes 1 votes Arjun commented Apr 19, 2022 reply Follow Share Is the given statement true only for a singleton domain and false for every other domain? 0 votes 0 votes shishir__roy commented Apr 19, 2022 reply Follow Share Yes, for every domain with more than 1 element the statement will be False. And for every singleton domain the statement will be True. 2 votes 2 votes Please log in or register to add a comment.