relation and functions

Let R be the relation in the set N given by R = {(a,b); a = b – 2 , b > 6} Is the relation reflexive?

• yes

• no

The smallest equivalence relation R on set A = {1,2,3} is

• {(1,1) ,(2,2),(3,3)}

• {(1,1) ,(2,2),(3,3),(1,2),(2,1)}

• {(1,1) ,(2,2),(3,3), (2,1)}

• none of these

Let R be the relation in the set of natural numbers N defined as

R = {(x,y) ϵ N x N : 3x +y =11}. Then R^-1 is given by

• {(0,11),(1,8), (2,5),(3,2)}

• {(1,8),(2,5),(3,2)}

• {(11,0),(8,1),(5,2),(2,3)}

• {(8,1),(5,2),(2,3)}

Tags

CCSS.HSF-BF.B.4A

The domain of function y= sin^-1(-x²) is

• [0,1]

• (0,1)

• [-1,1]

• none of these

Tags

CCSS.HSF-BF.B.4D

The domain of y =cos^-1 (x² - 4) is

• [3,5]

• [0,π]

• [-1,1]

• none of these

Given triangles with sides T₁: 3,4,5 ; T₂ : 5,12,13 ; T₃:6,8,10 ; T₄ : 4,7,9 and a relation R in the set of triangles define as

R = { (Δ_1, Δ_{2) :} Δ₁ is similar to Δ₂ . Which triangles belong to the same equivalence class ?

• T₁ and T₂

• T₂ and T₃

• T₁ and T ₃

• none of these

Tags

CCSS.HSG.SRT.A.2

Let R be a relation on the set L of lines defined by l₁ R l₂ if l₁is perpendicular to l₂, then relation R is

• reflexive and symmetric

• symmetric and transitive

• equivalence relation

• symmetric

Tags

CCSS.8.EE.C.8C

Let f: R- {2} → R –{1} be a function defined by

f(x) = (x -1) / (x- 2) , then f is

• into function

• many one function

• bijective function

• many one, into function

Tags

CCSS.HSF-BF.B.4D

Given set A = {a,b,c}. An identity relation in set A is

• R= {(a,b),(a,c)}

• R = {(a,a),(b,b), (c,c) }

• R= {(a,a),(b,b), (c,c), (a,c)}

• R= {(c,a),(b,a), (a,a)}

Let A = {a,b} . Then number of one-one function from A to A possible are

• 1

• 2

• 3

• 4