Please answer both if possible! thank you! 11.JLet H(x) be \"r can ski\", S(x) b

Question

Please answer both if possible! thank you!

11.JLet H(x) be "r can ski", S(x) be "r can skate", W(x) be "r loves winter" and P(x) be "r plays soccer". The universe of discourse is all humans. State the following logically. (a) No one who can ski plays soccer. (b) At least one person who does not love winter can skate (c) Not everyone loves winter. (d) There is exactly one person who can skate and can ski. 12. Express the negation of the following statements: (a) All wireless network connections do not have the same bandwidth (b) There is at least one person in Carleton who does not know logic.

Explanation / Answer

A= universal quantifier e- existential

1 a) (Ax) H(x) => ~ P(x)   

for all x where x can ski, then he does not play soccer

b) (Ex) ~W(x) ^S(x)

There exists a person who does not love winter and can skate

c) (Ex) ~W(x)

There exists someone.. who does not like winter

d) (Ex) H(x) ^ S(x)

There exists one person who can skate and ski

2a) Let WC(x) be "wireless network connection" and B(x,y) be "x and y have same bandwidth"

(E WC(x))(E WC(y)) ^ ~ B(x,y)

There exists a wireless connection x and y and they dont have same bandwidth

b) Let P(x)= x is a person C(x)= x is in Carleton and L(x) be x knows logic

(E P(x)) ^ C(x) ^ ~L(x)

There exists a person x and x is in Carleton and x does not know logic

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