The following was said in a charity appeal on Radio 4 in October 2006.
"It is hard to underestimate the effect that your contribution will make."
Rewrite the comment more simply in your own words without changing its meaning.
A machine has three components, A, B and C, each of which is either active or inactive.
The machine is active if A and B are both active.
The machine is active if A is inactive and C is active.
The machine is active if B is inactive and C is active.
Otherwise the machine is inactive.
The states (active or inactive) of the components and the machine are to be modelled by a combinatorial circuit in which "active" is represented by "true" and "inactive" is represented by "false".
Draw such a circuit.
Construct a truth table to show the following.
$$[ ( ( \mathrm { a } \wedge \mathrm {~b} ) \vee ( ( \sim \mathrm { a } ) \wedge \mathrm { c } ) ) \vee ( ( \sim \mathrm { b } ) \wedge \mathrm { c } ) ] \Leftrightarrow \sim [ ( ( \sim \mathrm { a } ) \wedge ( \sim \mathrm { c } ) ) \vee ( ( \sim \mathrm { b } ) \wedge ( \sim \mathrm { c } ) ) ]$$