If ‘A * B’ means ‘A is the mother of B’ and ‘A × B means ‘A is the husband of B’, which of the following shows ‘P is the father of Q’?
Question
If ‘A * B’ means ‘A is the mother of B’ and ‘A × B’ means ‘A is the husband of B’, which of the following shows ‘P is the father of Q’?
Solution
To show 'P is the father of Q' using the given symbols, we need to find a way to express 'P is the husband of someone and that someone is the mother of Q'.
Step 1: We know that 'A * B' means 'A is the mother of B'. So, we can use '* Q' to represent 'the mother of Q'.
Step 2: We also know that 'A × B' means 'A is the husband of B'. So, we can use 'P ×' to represent 'P is the husband of'.
Step 3: Combining these two, we get 'P × (* Q)', which means 'P is the husband of the mother of Q', or in other words, 'P is the father of Q'.
So, 'P × (* Q)' is the expression that shows 'P is the father of Q'.
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