Suppose A.B = A.C, what can you deduce about A, B and C?
From the given equation A.B = A.C, we can deduce that A is not equal to zero, as otherwise the equation would not hold.
However, we cannot deduce any specific information about B and C. We only know that whatever values B and C have, their product will be equal when multiplied with A.
If A.B = A.C, we can deduce the following:
1. A does not equal zero: Since A is a common factor on both sides of the equation, if A were zero, the equation would not hold true. Therefore, A must be a non-zero value.
2. A.B - A.C = 0: By subtracting A.C from both sides of the equation, we get A.B - A.C = 0. This can be further simplified as A(B - C) = 0.
3. B - C = 0: Since A is non-zero, the only way for the product A(B - C) to be equal to zero is if the factor (B - C) is equal to zero. So, we can conclude that B must be equal to C.
To summarize, from the given equation A.B = A.C, we can deduce that A is non-zero, and B is equal to C.