Let the propositional function C (f,a) mean "The function f is continuous at the point a," and let the propositional function of D(f,a) mean "The function f is differentiable at the point a" Using these symbols together with logical symbols, express the following statements.

Question

usukidoll · Answer

Neither the tangent function nor the secant function is continuous at pi/2.
Either a>0 or the natural logarithm function is not differentiable at a.
The absolute value function is continuous at 0, but not differentiable at 0.

usukidoll · Answer

so for the first one I got that the sentence is related to C f(a,) because the functions are tangent and secant. 
I should write it as ~C(f,a) but is just ~C(f,a)?

usukidoll · Answer

Second one. D(f,a) related. it says that either a>0 or the natural logarithm function is not differential at a. 
if I didn't have the c(f,a) d(f,a) required I would easily put my P as a>0 and Q that long sentence and that would be P V Q.

usukidoll · Answer

Third one is again D(f,a) related. 
The absolute value function is continuous at 0, but not differentiable at 0.
with my p = absolute value function is continuous at 0
q = not differentiable at 0
this is not an implies or bi-conditional.

usukidoll · Answer

P ^ Q
but that would read as The absolute value function is continuous at 0, [and] not differentiable at 0.

usukidoll · Answer

but thing is how to apply the C(f,a) and D(f,a) in this?

ganeshie8 · Answer

For second question :-
Either a>0 or the natural logarithm function is not differentiable at a.

(a >0)  V  ~D(ln, a <= 0)

usukidoll · Answer

OH OF COURSE! *facepalm*
we have to apply the f a in the C or D

usukidoll · Answer

The absolute value function is continuous at 0, but not differentiable at 0.
The ORIGINAL D(f,a) states  "The function f is differentiable at the point a"
F not differentiable at 0 . .  . hmm there's no point a

usukidoll · Answer

the first one for C(f,a) f would be neither tangent nor secant a is continous at pi/2

ganeshie8 · Answer

The absolute value function is continuous at 0, but not differentiable at 0.

C(f, 0) ^ ~D(f, 0)

ganeshie8 · Answer

you want to translate the given statements to boolean symbols. thats all right ?

usukidoll · Answer

errr it did say that I have to use those special symbols... if I didn't have to, I can easily see the P and Q 's

ganeshie8 · Answer

wat special symbols ?

usukidoll · Answer

so all of C(f,a) is negated on this.

usukidoll · Answer

Let the propositional function C (f,a) mean "The function f is continuous at the point a," and let the propositional function of D(f,a) mean "The function f is differentiable at the point a" Using these symbols together with logical symbols, express the following statements.

ganeshie8 · Answer

i have read that before

usukidoll · Answer

Neither the tangent function nor the secant function is continuous at pi/2 is purely a negative C (f,a) for f being tangent function nor secant function and a continuous at pi/2

ganeshie8 · Answer

First one :

Neither the tangent function nor the secant function is continuous at pi/2 is 
~C(tan, pi/2) ^ ~C(sec, pi/2)

usukidoll · Answer

thought so...so I have to make it into detail as everything counts.

ganeshie8 · Answer

just convert the statemetns, whats big deal ha

ganeshie8 · Answer

unless we both are not in same page... :o

usukidoll · Answer

well I quickly saw the first one as a double negative. no no it did say to use C f,a and D f,a Which I sort of seen. except the last one was a tad tricky

ganeshie8 · Answer

for me, first and last are easy. middle one is tricky as we need to think a bit

usukidoll · Answer

k new practice question.