Final answer:
The context of the student's question is unclear, mixing truth tables with algebraic equations. The response clarifies the conditions under which equality holds in algebraic expressions and emphasizes the importance of non-zero factors and performing operations evenly on both sides of an equation.
Step-by-step explanation:
The student appears to be confused about the context of the problem, as the request for a truth table is more relevant to logic and computer science, particularly when dealing with Boolean algebra. However, based on the snippets, including equations and the use of variables, it seems they are trying to understand algebraic properties and possibly preparing for examples involving variables or scientific laws in different scenarios. We can attempt to clear up the confusion by systematically addressing each equation in the snippets provided, although they seem to be incomplete and might come from different contexts.
For example, when looking at equation (a), we cannot conclude A = B from A × F = B × F unless we know that F is not equal to zero. Multiplying both sides by a non-zero number doesn't change the equality. However, if we multiply by zero, both sides will be zero regardless of the values of A and B, which means we cannot conclude that A and B are equal.
In the case of the second equation, the presence of variables and unknowns is clear, but the context is not. Still, to find an unknown in an equation with multiple variables, one must have either a single variable or enough equations to solve for the variables present. This is related to solving systems of linear equations or using substitution to isolate one variable.
Lastly, statements like 'Whatever you want to do, just do it to both sides' refer to the fundamental property of being able to perform the same operation on both sides of an equation without affecting the equality, which is an essential strategy for solving algebraic equations.