3. When translating from mathematical symbols to English sentences, first translate each symbol into English and read that in the order it appears to get the meaning of the sentence. Then write a proper English sentence with the same meaning as the mathematical sentence. Note that when translating mathematics into English, there are usually many correct answers. Your answers should have the same meanings as the answers below.
a) A first attempt at translation might give you something like: For all
squares s, s is a rectangle. Rewriting this you might end up with:
All squares are rectangles.
b) A first attempt at translation might give you
something like: There exists a real number x such that x is a rational number. Rewriting
this you might end up with:
There is a real number which is also a rational number.