Mathematics
Equivalence relation
Practice questions
An equivalence relation on a set (A) has class sizes (1,2,4). If (A) has (7) elements, how many ordered pairs are in the relation?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}). Which relation is this?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)}). Why is this not an equivalence relation?On all real numbers, (aRb) if and only if (a-b) is an integer. Choose the correct statement about (0.25) and (3.25).On all positive real numbers, (aRb) if and only if (\log a-\log b\in Z). Which is the equivalence class of (1)?On (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) leave the same remainder on division by (2). What is the quotient set (A/R)?On the set of all rectangles, (R_1RR_2) if and only if the two rectangles have the same area. What type of relation is this?On (A={1,2,3,4,5}), (aRb) if and only if (a+b=6). Is this an equivalence relation?If (R) and (S) are equivalence relations on the same set (A), which statement about (R\cap S) is correct?If (R) and (S) are equivalence relations, which statement is generally true about (R\cup S)?On (A={1,2,3,4,5,6}), (aRb) if and only if (a) and (b) are both multiples of (2) or both not multiples of (2). Which is the equivalence class of (5)?On natural numbers, (aRb) if and only if (a) and (b) have the same sum of digits. Which of the following is in the equivalence class of (29)?On all real numbers where tangent is defined, (aRb) if and only if (\tan a=\tan b). Which of the following is in the equivalence class of (0)?On (A={1,2,3,4,5}), (aRb) if and only if (a=b) or (a+b=6). Is this an equivalence relation?For the relation (aRb) if and only if (a=b) or (a+b=6) on (A={1,2,3,4,5}), which is the correct partition?On positive integers, (aRb) if and only if (a) and (b) have the same last digit. What forms the equivalence class of (102)?If an equivalence relation has classes ({1,2}), ({3,4,5}), and ({6}), which statement about ((2,5)) and ((4,3)) is correct?On all real numbers, (aRb) if and only if (|a|+|b|=0). Is this an equivalence relation?Which of the following relations on the set of integers \(\mathbb{Z}\) is an equivalence relation?On (A={1,2,3,4,5}), (aRb) if and only if the squares of (a) and (b) leave the same remainder on division by (5). Which is the equivalence class of (2)?