##
Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line 𝑦 = 𝑥 − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

##
**
Question 1
**

##
Let relation R be defined by R = {(L
_{
1
}
, L
_{
2
}
) : L
_{
1
}
∥ L
_{
2
}
where L
_{
1
}
, L
_{
2
}
∈ L}

then R is______ relation

(a) Equivalence

(b) Only reflexive

(c) Not reflexive

(d) Symmetric but not transitive

##
**
Question 2
**

##
Let R = {(L
_{
1
}
, L
_{
2
}
) ∶ L
_{
1
}
⊥ L
_{
2
}
where L
_{
1
}
, L
_{
2
}
∈ L} which of the following is true?

(a) R is Symmetric but neither reflexive nor transitive

(b) R is Reflexive and transitive but not symmetric

(c) R is Reflexive but neither symmetric nor transitive

(d) R is an Equivalence relation

##
**
Question 3
**

##
The function f:
**
R
**
→
**
R
**
defined by 𝑓(𝑥) = 𝑥 − 4 is___________

(a) Bijective

(b) Surjective but not injective

(c) Injective but not Surjective

(d) Neither Surjective nor Injective

For Proof, Check Example 2 – Chapter 1 Class 12

##
**
Question 4
**

##
Let 𝑓: 𝑅 → 𝑅 be defined by 𝑓(𝑥) = 𝑥 − 4. Then the range of 𝑓(𝑥) is ________

(a) R

(b) Z

(c) W

(d) Q

##
**
Question 5
**

##
Let R = {(L
_{
1
}
, L
_{
2
}
) : L
_{
1
}
is parallel to L
_{
2
}
and L
_{
1
}
: y = x – 4} then which of the following can be taken as L
_{
2
}
?

(a) 2x – 2y + 5 = 0

(b) 2x + y = 5

(c) 2x + 2y + 7 = 0

(d) x + y = 7