Four students present the following arguments to justify that only one straight line passes through two given points P and Q.
I. If two different lines pass through P and Q, then both lines coincide at P and Q, so they are identical; this is a contradiction.
II. Euclid’s Postulate 1 states that only one line can be drawn through two distinct points; hence uniqueness is proven.
III. From point P, infinitely many lines can be drawn; selecting one passing through Q suffices, but another different line might also pass through Q.
IV. Using Postulate 1 and Common Notion 1, if two lines coincide at two points, they must be the same line.
Which of the above arguments constitute a valid deductive proof of uniqueness?
a) II and IV only
b) I and II only
c) I and IV only
d) I, II and IV