Explain the distinction between the compound propositions, \(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q\) and \(p \vee q\).

Fill in the four missing truth-values on the table.

State whether the proposition \(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q \Rightarrow \neg p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } \neg q\) is a tautology, a contradiction or neither.

Both are 'p or q', the first is 'but not both'     (A1)

Note: Award mark for clear understanding if wording is poor.     (C1)

[1 mark]

     (A1)(A1)(ft)(A1)(A1)

Note: Follow through is for final column.     (C4)

[4 marks]

Tautology.     (A1)(ft)     (C1)

[1 mark]

a) The majority of candidates were able to explain the difference between inclusive and exclusive correctly but many used “and” and “or” to distinguish between the two.

b) Less than half were able to find the truth value of the two disjunctions in the table correctly. Most candidates did gain some marks but a number of them left at least one cell blank even though it was a 50% chance of getting the correct value.

c) Most candidates answered this part correctly with many receiving follow through for “neither” from an incorrect table.