I need someone to help me solve these 4 assignments. Thank you 1. Use truth tabl
ID: 3143682 • Letter: I
Question
I need someone to help me solve these 4 assignments. Thank you
1. Use truth tables to prove that the following are equivalent:
(a) ( ) and ()
(b) ( ) and ( ) ( )
(c) ( ) and ( ) ( )
Verify the equivalences in (b) and (c) in the previous question by means of
a logical argument. (So, in the case of (b), for example, you must show that
assuming and deducing is the same as both deducing from and
from .)
2.Use truth tables to show that and are not equivalent. Give an
example of statements and such that is true but is false.
3.Identify the antecedent and the consequent in each of the following
conditionals:
(a) If apples are red then oranges are green.
(b) The differentiability of a function f is sufficient for f to be continuous.
(c) A function f is bounded if f is integrable.
(d) A sequence s is bounded whenever s is convergent.
(e) It is necessary that n is prime in order for 2n 1 to be prime.
(f) The team wins only when Karl is playing.
(g) When Karl plays the team wins.
(h) The team wins when Karl plays.
4.Which of the following pairs of propositionals are equivalent?
(a) (P Q),P Q
(b) P Q,(P Q)
(c) (P Q),P Q
(d) (P (Q R)),(P Q)(P R)
(e) P (Q R), (P Q) R
Explanation / Answer
3) Antecedent is the statment which is presumed to be true for another statement (consequent) which is dependent on Antecedent and may be true or false based on the truthness of Antecendent.
(a) If apples are red then oranges are green.
apples are red is Antecedent , oranges are green is consequent
b) f is dfferenciable is Antecedent , f is continuous is consequent
(c) A function f is bounded is consequent , f is integrable is Antecedent
(d) A sequence s is bounded is consequent , s is convergent is Antecedent
(e) n is prime is Antecedent , 2n 1 is prime is Consequent
(f) Karl is playing is Antecedent , The team wins is consequent
(g) Karl plays tis Antecedent ,the team wins is consequent
(h) The team wins is consequent , Karl plays is Antecedent
4) the following pairs of propositionals are equivalent-
(a) (P Q),P Q
(c) (P Q),P Q
Reason- By demorgans law, the statements are equivalent.