Mathematics
Equivalence relation
Practice questions
On (A={1,2,3,4,5,6,7,8}), (aRb) if and only if (a) and (b) leave the same remainder when divided by (4). Which elements are in the equivalence class of (2)?On the set of all triangles, (T_1RT_2) if and only if (T_1) and (T_2) are similar. What type of relation is this?If (R) is an equivalence relation on a set (A) and (aRb), what is true about the equivalence classes of (a) and (b)?If (R) is an equivalence relation on a set (A), which statement is true about two distinct equivalence classes?On (A={1,2,3,4}), (aRb) if and only if (a=b). How many equivalence classes does this relation have?On the set of real numbers, (aRb) if and only if (\lfloor a\rfloor=\lfloor b\rfloor). Which is the equivalence class of (2.4)?On integers, (aRb) if and only if (a-b) is divisible by (4). Which is the equivalence class of (-1)?On all subsets of (A={1,2,3,4}), (XRY) if and only if (|X|=|Y|). How many subsets are in the equivalence class of ({1,2})?On real numbers, (aRb) if and only if (a^3=b^3). Choose the correct statement about this relation.On the set of all lines in a plane, (lRm) if and only if (l) and (m) have the same direction. What do the equivalence classes represent?On (A={1,2,3,4,5,6,7,8,9}), (aRb) if and only if (a) and (b) leave the same remainder when divided by (3). How many ordered pairs are in this relation?On real numbers, (aRb) if and only if (\sin a=\sin b). Is this relation an equivalence relation?On (A={1,2,3,4,5}), (R={(a,b):|a-b|\text{ is even}}). What is the equivalence class of (4)?On the set of all polynomials with real coefficients, (pRq) if and only if (p(0)=q(0)). What type of relation is this?On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}) is given. Why is it not an equivalence relation?If (A) has (5) elements and the partition of an equivalence relation is ({{a,b},{c,d,e}}), how many ordered pairs are in the relation?On non-zero integers, (aRb) if and only if (ab>0). How many equivalence classes are formed by this relation?On the set of all circles, (C_1RC_2) if and only if the two circles have the same radius. What type of relation is this?On (A={1,2,3,4,5,6}), (aRb) if and only if (a+b) is divisible by (2). What are the equivalence classes of this relation?On the set (R^2) of all ordered pairs, ((a,b)S(c,d)) if and only if (a+c=b+d). Is (S) an equivalence relation?