Complete the following statements. 1. a conjunction is true (only if both statements are true, if at least one statement is true) 2. a disjunction is true (only if both statements are true, if at least one statement is true) 3. for a conditional statement, a (false hypothesis cannot imply a true conclusion, true hypothesis cannot imply a false conclusion)

The conjunction is the AND logical operator, and the result of A AND B is true only when both A and B are true. For example, "We are on planet earth, and elephants fly" is false, even if the first part is actually true.

In fact, the disjunction is the OR operator, and this time one true statement is sufficient to make the whole expression true: "You are reading this answer on or I am 4 meters tall" is true, although I'm not 4 meters tall.

In fact, the latin expression "ex falso sequitur quodlibet" translates as "you can deduce whatever you want from a false premise". Using formulas, this means that the implication is always true, no matter the truth value of B. So, both these implications

are true.

Conversely, if the hypothesis is true, then the implication is true only if the conclusion is true as well: if we change the previous example to

Only the second implication will hold.

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