| Date | May 2014 | Marks available | 2 | Reference code | 14M.1.sl.TZ1.14 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Express | Question number | 14 | Adapted from | N/A |
Question
Two propositions are defined as follows:
\(p:\) Quadrilateral ABCD has two diagonals that are equal in length.
\(q:\) Quadrilateral ABCD is a rectangle.
Express the following in symbolic form.
“A rectangle always has two diagonals that are equal in length.”
Write down in symbolic form the converse of the statement in (a).
Determine, without using a truth table, whether the statements in (a) and (b) are logically equivalent.
Write down the name of the statement that is logically equivalent to the converse.
Markscheme
\(q \Rightarrow p\) (A1)(A1) (C2)
Note: Award the first (A1) for seeing the implication sign, the second (A1) is for a correct answer only. Not using the implication earns no marks.
[2 marks]
\(p \Rightarrow q\) (A1)(ft) (C1)
Note: Award (A1)(ft) where the propositions in the implication in part (a) are exchanged.
[1 mark]
Not equivalent; a kite or an isosceles trapezium (for example) can have diagonals that are equal in length. (A1)(R1) (C2)
Notes: Accept a valid sketch as reasoning.
If the reason given is that a square has diagonals of equal length, but is not a rectangle, then award (R1)(A0).
Do not award (A1)(R0).
Do not accept solutions based on truth tables.
[2 marks]
Inverse (A1) (C1)
Note: Do not accept symbolic notation.
[1 mark]
