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Class 12 · Mathematics
→On (A={1,2,3,4}), (R=A\times A). Which statement about its equivalence classes is correct?
Class 12 · Mathematics
→If two equivalence classes (B_1) and (B_2) of an equivalence relation satisfy (B_1\cap B_2\neq \varnothing), what conclusion follows?
Class 12 · Mathematics
→On natural numbers, (aRb) if and only if (a) and (b) have the same set of prime factors. Which of the following belongs to the equivalence class of (12)?
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→On non-zero integers, (aRb) if and only if (ab>0). How many equivalence classes are formed by this relation?
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→On the set of all polynomials with real coefficients, (pRq) if and only if (p(0)=q(0)). What type of relation is this?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (R={(a,b):|a-b|\text{ is even}}). What is the equivalence class of (4)?
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (\sin a=\sin b). Is this relation an equivalence relation?
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (a^3=b^3). Choose the correct statement about this relation.
Class 12 · Mathematics
→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})?
Class 12 · Mathematics
→On integers, (aRb) if and only if (a-b) is divisible by (4). Which is the equivalence class of (-1)?
Class 12 · Mathematics
→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)?
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if (a=b). How many equivalence classes does this relation have?
Class 12 · Mathematics
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