Mathematics
Reflexive relation
Practice questions
If (A={1,2,3,4}), how many reflexive relations have exactly (2) non-diagonal pairs and ((1,2)) is one of them?On a five-element set, how many reflexive relations are neither the identity relation nor the universal relation?If (A={1,2,3,4}), how many reflexive relations contain exactly (11) ordered pairs?On (A={1,2,3,4,5}), a relation has exactly (18) pairs and is reflexive. How many pairs are present besides the compulsory diagonal pairs?If (S={1,2,3,4}) and (A=\mathcal{P}(S)), how many reflexive relations are possible on (A)?On (A={\varnothing,{1},{2},{1,2}}), (R={(X,Y):X\subset Y\text{ or }X\cap Y=X}). What is the correct conclusion about (R)?If (A={1,2,3,4,5,6}) and ((a,b)\in R) only when (a) and (b) have a common prime factor, is (R) reflexive?On (A={2,3,4,5,6,7}), ((a,b)\in R) if (a) and (b) have a common prime factor. How many diagonal pairs are in (R)?If (A={1,2,4,8,16}) and (R={(a,b):\frac{b}{a}\text{ is an integral power of }2}), why is (R) reflexive?On (A={1,2,3,4,6,12}), (R={(a,b):a\mid b\text{ or }b\mid a}). What is the reason for (R) being reflexive?If (A={1,2,3,4,5}) and (R={(a,b):a+b=ab}), how many diagonal pairs are in (R)?On (A={1,2,3,4,5}), (R={(a,b):a+b=ab}). How many pairs must be added to make (R) reflexive?If (A={0,1,2,3,4}) and (R={(a,b):a^2-a=b^2-b}), why is (R) reflexive?On (A={0,1,2,3,4,5}), (R={(a,b):a^2+b^2=2ab}). Which statement about (R) is correct?If (A={1,2,3,4,5}) and (R={(a,b):a^2+b^2<2ab}), is (R) reflexive?On (A={1,2,3,4,5,6}), (R={(a,b):a-b\text{ is divisible by }7}). What fact proves that (R) is reflexive?If \(f(x)=x^2+1\) and \(g(x)=x-1\), what is \((f\circ g)(3)\)?If \(f(x)=2x+3\) and \(f(a)=11\), what is the value of \(a\)?If \(f(x)=kx-3\) and \(f(4)=17\), what is the value of \(k\)?Let (f:\mathbb{R}\to[0,\infty)) be defined by (f(x)=x^2+2x+1). When will (f) be considered onto?