1)lndicate whether the following statements are true or false:
a)lt can not proved mathematically that 2+2=4
b)It can be proved that there is no paradox in mathematics.(give an example)
c)Hilbert proved that thereis a statement in matematics whicah is true but can not be proved
d) Gödel proved that there is a statement in mathematics which can neither be proved nor pisproved
2)We toss a fair coin.Below 'H' denotes heads and 'T' denotes tails.What is the probability that:
a)We get HHT in the first three tosses?
b)We get two H and a T (in any order) in three tosses?
c)We get all H in the first n tosses?
d)We get HT in the 12nd and 13th tosses,respectively,if we toss the coin 15 times?
e)We get the squence HTTH eventually (i.e if we toss the coin infinitely many times)?
3)What was the set that Russell used to show that there was a paradox in mathematics?
Thank you so much I am waiiting for your msg guys..
Too many questions, too little self work shown. What have you done and where're you stuck?