course Mth 151
March 23 around 3
Mary Sholesassignment17-QA
q001:
This phrase has to be true because r is true. The truth table that is distinguished by this look like: TTT, TFT, FTT, FFT.
*2 on confidence scale
q002:
TTF tells us that one of the statements are false, but that just means that [(p->q)^(q -> r)^p] -> r is true.
*2 on confidence scale
q003:
TTF does tell us that the statement q->r is false because both p and q are true. So therefore this makes [(p -> q)^(q -> r)^p]false.
*2 on confidence scale
q004:
In the case TFF: p is true and q is false so p->q is false. In the case FTF: p is false. In the case FFF: p is false. So therefore, [(p->q) ^(q->r)^p]and[(p->q)^(q->r)^p]and[(p->q)^(q->r)^p]are all false.
*2 on confidence scale
q005:
Because it would be true everytime r is false.
*2 on confidence scale
q006:
When r is true, the statement is always true.
*2 on confidence scale
q007:
this is valid because the statement is always true and never false.
*2 on confidence scale
q008:
This argument can be symbolized by letting p stand for 'it snows', q for 'the roads are slippery', r for 'the roads are safer to drive on'. Then'If it snows, the roads are slippery' is symbolized by p -> q.
'If the roads are slippery they'll be safer to drive on' is symbolized by q -> r. 'It just snowed' is symbolized by p. 'The roads are safer to drive on' is symbolized by r. This statement is true because r is true and that is the rule!
*2 on confidence scale
q009:
let p stand for 'it rained', q for 'there is a picnic'. The first statement is 'If it doesn't rain there is a picnic', which is symbolized by ~p -> q. The second statement, 'There is no picnic', is symbolized by ~q. The conclusion, 'it rained', is symbolized by p. The argument therefore says IF [ (~p -> q) AND ~q ], THEN p. This is symbolized by [ (~p -> q) ^ ~q ] -> p.The truth table would look like this:
p q ~p ~q ~p -> q (~p -> q) ^ ~q [ (~p -> q) ^ ~q ] -> p
T T F F T F T
T F F T T T T
F T T F T F T
F F T T F F T
*2 on confidence scale
&#Please let me know if you have questions. &#