What does it take for a compound conditional statement to be false?

I need an explanation for the conjunction and the disjunction (inclusive or and exclusive or forms).What does it take for a compound conditional statement to be false?
Conjunctions are true only if both hypotheses are true. Otherwise, the compound conditional statement is false. The example that states ';If a figure is a parallelogram and has 4 right angles, then it's a rectangle,'; is a true conjunction. This is because a figure can be a parallelogram and have 4 right angles at the same time and be a rectangle. Both hypotheses are true. Therefore, the statement is true. However, an example of a false conjunction would be ';If a figure is a parallelogram and has at least 5 right angles, then it is a rectangle.'; We know the second hypothesis (at least 5 right angles) is false because a rectangle doesn't have 5 right angles. It has 4 right angles. Since the second hypothesis in the conjunction is false, the compound conditional statement is false.





Disjunctions that use the inclusive or, or the exclusive or are false only when both hypotheses are false. Otherwise, the compound conditional statement is true. The statement ';if a figure is a parallelogram or had 4 right angles, then it's a rectangle,'; is true. This is true because a rectangular figure can be a parallelogram and have 4 right angles at the same time. Since both hypotheses are true at the same time, this is considered to be written in the inclusive or format. If you had a statement that said, ';If an angle is less than 90 degrees or greater than 90 degrees, then it is not a right angle,'; then this would be a disjunction in the exclusive or format. We know this is the case because an angle cannot be less than 90 degrees and/or greater than 90 degrees at the same time. If one of the hypotheses is true, the disjunction is still true.





However, an example of a false disjunction would be if you said, ';If a figure is not a parallelogram and does not have 4 right angles, then it is a rectangle.'; Since a rectangle is a parallelogram and it does have 4 right angles, then the two hypotheses are false. Therefore the disjunction and the entire compound conditional statement are false.What does it take for a compound conditional statement to be false?
A inclusive or B is false if both A and B are false.





A exclusive or B is false if both A and B are either false or true (they cannot both be true, that's the 'exclusive' part of things). It is true if just one of A or B is true.