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Class 12 · Mathematics

On real numbers, (aRb) iff (|a|=|b|). What type of relation is it?

Class 12 · Mathematics

On real numbers, (aRb) iff (a^2\le b^2). Which statement is correct?

Class 12 · Mathematics

On real numbers, (aRb) iff (a^3=b^3). What type of relation is it?

Class 12 · Mathematics

On real numbers, (aRb) iff (a-b) is irrational. Which statement is correct?

Class 12 · Mathematics

On real numbers, (aRb) iff (a-b) is an integer. What type of relation is it?

Class 12 · Mathematics

On integers, (aRb) iff (a+2b) is divisible by (3). In which property does this relation fail?

Class 12 · Mathematics

On integers, (aRb) iff (a-b) is divisible by (6). What is the equivalence class of (7)?

Class 12 · Mathematics

On (A={1,2,3,4}), how many equivalence relations have exactly one class of size (2) and all other classes singleton?

Class 12 · Mathematics

On (A={1,2,3,4,5}), how many equivalence relations have one class of size (2) and the other of size (3)?

Class 12 · Mathematics

On (A={1,2,3,4}), how many equivalence relations have exactly two equivalence classes?

Class 12 · Mathematics

If (A) has (4) elements, how many equivalence relations can be formed on (A)?

Class 12 · Mathematics

How many relations on (A={1,2,3,4}) are reflexive, symmetric and antisymmetric all together?

Class 12 · Mathematics

How many relations on (A={1,2,3,4}) are both symmetric and antisymmetric?

Class 12 · Mathematics

If (A) has (5) elements, what is the number of relations on (A) that are both reflexive and antisymmetric?

Class 12 · Mathematics

If (A) has (4) elements, how many antisymmetric relations can be formed on (A)?

Class 12 · Mathematics

If (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4),(1,4)}) on (A={1,2,3,4}), which statement about (R) is false?

Class 12 · Mathematics

If (R) is symmetric on (A={1,2,3}) and ((1,3)) is in (R\circ R), what type of chain may be possible?

Class 12 · Mathematics

How many ordered pairs does the equivalence relation with classes {1,2} and {3,4} contain?

Class 12 · Mathematics

If the classes of (R) on (A={1,2,3,4}) are ({1,2}) and ({3,4}), which pair must be in (R)?

Class 12 · Mathematics

If (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,4),(4,3)}) on (A={1,2,3,4}), which partition is formed by (R)?