Necessary versus Sufficient Conditions: Self-Test Answers

T        F     1.  Being a mammal is a sufficient condition for being human.  False.  Being a mammal does not guaranteee that one is a human.  There are mammals that are not human.

T        F     2.  Being human is a sufficient condition for being a mammal.  True.  Being a human guarantees that one is a mammal.  As soon as we find out that something is not a mammal, we know that it cannot be a human.

T        F     3.  Being alive is a necessary condition for having a right to life.  True.  Nothing that is not alive can have a right to life.

T        F     4.  Being alive is a suffcient condition for having a right to life.  False.  There are lots of things that are alive that do not have a right to life.  What about, for example, grass?  This answer could be questioned by those who think that it is seriously wrong to kill anything that is alive.

T        F     5.  If it is true that if P then Q,  then P is a sufficient condition for Q.  True.  The truth of P is sufficient for, guarantees the truth of Q.

T        F     6.  If it is true that if P then Q, then Q is a necessary condition for P.  True.  If Q is not true, then P is not true.  The falsity of Q rules out the truth of P.  It is necessary for Q to be true in order for P to be true.

T        F     7.  If it is true that if P is not the case, then Q is not the case, then P is a necessary condition for Q.  True.  The truth of P is necessary in order for Q to be true.  When P is not true, Q is not true.

T        F     8.  If it is true that if P is not the case, then Q is not the case, then P is a sufficient condition for Q.  False.  The truth of P does not guarantee the truth of Q.  All we know is that the falsity of P guarantees the falsity of Q.  For example, let P be "A student hands in his/her term paper" and Q be "This student gets an A in 341."

T        F     9.   Something is a brother if and only if it is a male sibling.  This means that being a male sibling is both necessary and sufficient for something to be a brother.    True.  In general if it is the case that P is true if and only if Q is true, then Q is necessary and sufficient for P and P is necessary and sufficient for Q.   If anything fails to be male or fails to be a sibling, then it is not a brother.   So being a male sibling is a necessary condition for being a brother.  Furthermore, it is impossible for anything to be a male sibling and not to be a brother.  So being a male sibling is a sufficient condition for being a brother.