Currently a lecturer at the University of Science and Technology.
Express the negation of these propositions using quantifiers, and then express the negation in English.a) Some drivers do not obey the speed limit.b) All Swedish movies are serious.c) No one can keep a secret.d) There is someone in this class who does not have a good attitude.
Express the negation of each of these statements in terms of quantifiers without using the negation symbol.a) $\forall x(x>1)$b) $\forall x(x \leq 2)$$\begin{array}{ll}\text { c) } & \exists x(x \geq 4)\end{array}$d) $\exists x(x<0)$e) $\forall x((x<-1) \vee(x>2))$f) $\exists x((x<4) \vee(x>7))$
Find the area of each triangle having vertices at $P, Q,$ and $R$$$P(0,0), Q(0,2), R(1,4)$$
Find the area of each triangle having vertices at $P, Q,$ and $R$$$P(0,1), Q(2,0), R(1,5)$$
Find the area of each triangle having vertices at $P, Q,$ and $R$$$P(2,5), Q(-1,3), R(4,0)$$
