Lines a and b have different y-intercepts. When line a is

Upon request, I am providing the solution of the question above:
I will provide a graphical approach since that is what I favor always but later will give an algebraic approach too...

The two diagrams below illustrate the case where we take both statements together. In one case, reflection of a is not parallel to b and in the other reflection of a is parallel to b. Hence even with both statements we cannot say whether reflection of a is parallel to b. Answer (E).



If a and b make 45 degrees angle with the y axis (as shown, technically I will not say that they are both making 45 degrees angle with y axis but let's not worry about it here), when a is reflected along y axis, its angle with y axis is still 45. In this case a and b are parallel.

Algebraic approach:
A line is defined by 2 things - its slope and y intercept. When we reflect a line along the y axis, its slope flips sign but y intercept remains unchanged.

Now,
a -> y = mx + c
b -> y = nx + d
Reflected a -> y = -mx + c
Ques: Is -m = n? (Parallel lines have the same slope.)

Stmnt 1: mn = -1
m = -1/n.
If m = 1 and n = -1, -m is equal to n
If m = -1 and n = 1, -m is equal to n
If m = -1/2 and n = 2, -m is not equal to n
Not sufficient.

Stmnt 2: n>0
If m = -1 and n = 1, -m is equal to n
If m = -1/2 and n = 2, -m is not equal to n
Not sufficient.

Taking both together,
If m = -1 and n = 1, -m is equal to n
If m = -1/2 and n = 2, -m is not equal to n
Not sufficient. Answer (E).