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Class 12 · Mathematics
→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?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if (a=b) or (a+b=6). Is this an equivalence relation?
Class 12 · Mathematics
→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)?
Class 12 · Mathematics
→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)?
Class 12 · Mathematics
→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)?
Class 12 · Mathematics
→If (R) and (S) are equivalence relations, which statement is generally true about (R\cup S)?
Class 12 · Mathematics
→If (R) and (S) are equivalence relations on the same set (A), which statement about (R\cap S) is correct?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if (a+b=6). Is this an equivalence relation?
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→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)?
Class 12 · Mathematics
→On all positive real numbers, (aRb) if and only if (\log a-\log b\in Z). Which is the equivalence class of (1)?
Class 12 · Mathematics
→On all real numbers, (aRb) if and only if (a-b) is an integer. Choose the correct statement about (0.25) and (3.25).
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→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?
Class 12 · Mathematics
→On all integers, (aRb) if and only if (a) and (b) leave the same remainder on division by (10). Choose the correct statement about (27) and (-13).
Class 12 · Mathematics
→On the set of all vectors in (R^2), (uRv) if and only if (|u|=|v|). Which is the equivalence class of the zero vector?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6,7,8}), (aRb) if and only if (a) and (b) are of the same type: both less than (4) or both greater than or equal to (4). How many ordered pairs are there?
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (\cos a=\cos b). Which of the following numbers must be in the equivalence class of (0)?
Class 12 · Mathematics
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