Complete the truth table.

Consider the propositions p and q:

p: x is a number less than 10.

q: x2 is a number greater than 100.

Write in words the compound proposition \(\neg  p \vee  q\).

Using part (a), determine whether \(\neg p \vee q\) is true or false, for the case where \(x\) is a number less than 10 and \(x^2\) is a number greater than 100.

Write down a value of \(x\) for which \(\neg p \vee q\) is false.

(A1) for third column and (A1)(ft) for fourth column     (A1)(A1)(ft)     (C2)

\(x\) is greater than or equal to (not less than) 10 or \(x^2\) is greater than 100.     (A1)(A1)     (C2)

Note: Award (A1) for “greater than or equal to (not less than) 10”, (A1) for “or \(x^2\) is greater than 100”.

True     (A1)(ft)     (C1)

Note: Follow through from their answer to part (a).

Any value of \(x\) such that \( - 10 \leqslant x < 10\).     (A1)(ft)     (C1)

Note: Follow through from their answer to part (a).

This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false.

This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false. In part (c) many candidates either stated the correct answer “true” or stated an answer consistent with their truth table and received follow-through marks. Candidates had difficulty writing down a value of \(x\) for which \(\neg p \vee q\) is false.

This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false. In part (c) many candidates either stated the correct answer “true” or stated an answer consistent with their truth table and received follow-through marks. Candidates had difficulty writing down a value of \(x\) for which \(\neg p \vee q\]) is false.

This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false.