Write down in words the compound proposition

Complete the following truth table.

On a morning when Sandi does not get up before eight o’clock, use your truth table to determine whether \(p \Rightarrow (q{\text{ }}\underline  \vee  {\text{ }}r)\) is a tautology, contradiction or neither.

If Sandi gets up before eight o’clock then Sandi (either) goes for a run or goes for a swim, but not both.     (A1)(A1)(A1)     (C3)

Note:     Award (A1) for If …… then ……, (A1) for all propositions in the correct order, (A1) for “… or … but not both” (do not accept “either” as a replacement for “but not both”).

[3 marks]

     (A1)(A1)(ft)     (C2)

Note:     Award (A1) for correct \((q{\text{ }}\underline  \vee  {\text{ }}r)\) column, and (A1)(ft) for their correct \(p \Rightarrow (q{\text{ }}\underline  \vee  {\text{ }}r)\) column. Follow through from their \((q{\text{ }}\underline  \vee  {\text{ }}r)\) column.

[2 marks]

tautology     (A1)(ft)     (C1)

Note:     Follow through from part (b).

[1 mark]