Relations and Functions

Q1.The relation R = {(L1, L2): L1 is parallel to L2} on the set of all lines in the XY plane. The set of all lines related to y = 2x + 4 is

• AAll lines with slope 2
• BAll lines with y-intercept 4
• CAll vertical lines
• DAll horizontal lines

Q2.The Greatest Integer Function f: R -> R given by f(x) = [x] is

• AOne-one and onto
• BOne-one but not onto
• COnto but not one-one
• DNeither one-one nor onto

Q3.A function f: X -> Y is onto (surjective) if

• Af(x1) = f(x2) implies x1 = x2
• BRange of f = Y
• Cf is one-one
• DX and Y have the same number of elements

Q4.A function f: X -> Y is invertible if and only if f is

• AOne-one
• BOnto
• CBijective (one-one and onto)
• DA constant function

Q5.If f: R -> R is defined by f(x) = x^4, then f is

• AOne-one onto
• BMany-one onto
• COne-one but not onto
• DNeither one-one nor onto