Question

17-26

true or false questions

17. The smallest positive real number is c, where c = card(0,1). 18. To show that two sets A and B are equal, show that x A and x B. 19. If (vx)P(e) is false, then P(x) is never true for that domain. 20. If R is a relation on A and if (a, a) is true for some a in A, then R is reflexive. 21. If f:A → B is a function, then B = the range of f 22. The complex numbers of the form a +bi, where a and b are integers, is uncountable 23. If A is a countable set and if B is any infinite set, then card (A U B) -card(A). 24. If R is a relation from A to B and if S is a relation from B to C such that neither R nor S is a function, then S o R is not a function either. 25. A conjecture is the same as an open question. 26. Inductive proofs were used extensively by the ancient Greek geometers, like Euclid.

Answer 1

17.False.(There is no smallest positive real number) 18. False. 19.False. P(x) at be true for some x in the domain.) 20.False. aAa for every a E A must be satisfied.) 21.False. B is a superset of the range.) 22.False. au (y o r ut 23. False. (In this case card(AUB)card(B) 24.False. R can be a function. Example: A - {l), B- 2,3) , 4), R_ {(1.2), (1.3)〉,S={(2.1), (3.1)) C- Here Ro S is a function. 25.False. (it is a special case of open problem in which a result is stated which is apparently true with available examples but it is neither proved nor disproved by mathematical methods.) 26.False.