Easy -1.8 This question tests basic logical operations and truth tables, which are preliminary topics before group theory proper. Parts (a) and (b) are essentially non-mathematical warm-up exercises, while part (c) requires only mechanical construction of a truth table with standard logical operators—a routine A-level task requiring no problem-solving or insight.
The Plain English Society presents an annual "Foot in Mouth" award for "a truly baffling comment". In 2004 it was presented to Boris Johnson MP for a comment on the \(12 ^ { \text {th } }\) December 2003 edition of "Have I Got News For You":
"I could not fail to disagree with you less."
Explain why this can be rewritten as:
"I could succeed in agreeing with you more."
Rewrite the comment more simply in your own words without changing its meaning.
Two switches are to be wired between a mains electricity supply and a light so that when the state of either switch is changed the state of the light changes (i.e. from off to on, or from on to off). Draw a switching circuit to achieve this.
The switches are both 2-way switches, thus:
\includegraphics[max width=\textwidth, alt={}, center]{88acde67-e22b-478a-9145-48abe931beff-2_127_220_895_1054}
Construct a truth table to show the following.
$$[ ( a \wedge b ) \vee ( ( \sim a ) \wedge ( \sim b ) ) ] \Leftrightarrow [ ( ( \sim a ) \vee b ) \wedge ( a \vee ( \sim b ) ) ]$$
1
\begin{enumerate}[label=(\alph*)]
\item The Plain English Society presents an annual "Foot in Mouth" award for "a truly baffling comment". In 2004 it was presented to Boris Johnson MP for a comment on the $12 ^ { \text {th } }$ December 2003 edition of "Have I Got News For You":\\
"I could not fail to disagree with you less."
\begin{enumerate}[label=(\roman*)]
\item Explain why this can be rewritten as:\\
"I could succeed in agreeing with you more."
\item Rewrite the comment more simply in your own words without changing its meaning.
\end{enumerate}\item Two switches are to be wired between a mains electricity supply and a light so that when the state of either switch is changed the state of the light changes (i.e. from off to on, or from on to off). Draw a switching circuit to achieve this.
The switches are both 2-way switches, thus:\\
\includegraphics[max width=\textwidth, alt={}, center]{88acde67-e22b-478a-9145-48abe931beff-2_127_220_895_1054}
\item Construct a truth table to show the following.
$$[ ( a \wedge b ) \vee ( ( \sim a ) \wedge ( \sim b ) ) ] \Leftrightarrow [ ( ( \sim a ) \vee b ) \wedge ( a \vee ( \sim b ) ) ]$$
\end{enumerate}
\hfill \mbox{\textit{OCR MEI D2 2008 Q1 [16]}}