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Class 12 · Mathematics · Expert
→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 · Expert
→On (A={1,2,3,4}), (aRb) if and only if (a=b). How many equivalence classes does this relation have?
Class 12 · Mathematics · Expert
→If (R) is an equivalence relation on a set (A), which statement is true about two distinct equivalence classes?
Class 12 · Mathematics · Expert
→If (R) is an equivalence relation on a set (A) and (aRb), what is true about the equivalence classes of (a) and (b)?
Class 12 · Mathematics · Expert
→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?
Class 12 · Mathematics · Expert
→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)?
Class 12 · Mathematics · Expert
→On natural numbers, (aRb) if and only if (a) and (b) have the same unit digit. Which statement about this relation is correct?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1)}). Which partition is obtained from this relation?
Class 12 · Mathematics · Expert
→On the set of lowercase English alphabet letters, (aRb) if and only if (a) and (b) are both vowels or both consonants. How many equivalence classes does this relation form?
Class 12 · Mathematics · Expert
→On (A={1,2,3,4,5,6}), (aRb) if and only if (a\equiv b \pmod{3}). What are the distinct equivalence classes of this relation?
Class 12 · Mathematics · Expert
→On real numbers, (aRb) if and only if (a-b) is rational. Choose the correct statement about the equivalence classes of this relation.
Class 12 · Mathematics · Expert
→On (A={1,2,3,4}), (aRb) if and only if (a^2-b^2) is divisible by (3). What is the equivalence class of (1)?
Class 12 · Mathematics · Expert
→An equivalence relation on a set (A) has equivalence classes ({a,b,c}), ({d,e}), and ({f}). How many ordered pairs are there in this relation?
Class 12 · Mathematics · Expert
→A partition of (A={1,2,3,4}) is ({{1,4},{2},{3}}). How many ordered pairs will be in the equivalence relation formed by it?
Class 12 · Mathematics · Expert
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) is given. Which pairs are definitely needed to make it an equivalence relation?
Class 12 · Mathematics · Expert
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) is given. Which minimum pair must be added to make it an equivalence relation?
Class 12 · Mathematics · Expert
→On the set of non-zero real numbers, (aRb) if and only if (\frac{a}{b}>0). On what basis is this an equivalence relation?
Class 12 · Mathematics · Expert
→On integers, (aRb) if and only if (a+b) is even. Which of the following statements is correct?
Class 12 · Mathematics · Expert
→On the set (A={1,2,3,4,5}), (aRb) if and only if (a) and (b) are both even or both odd. How many blocks are formed in the partition by this relation?
Class 12 · Mathematics · Expert
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