Discrete Mathematics Answers

The Power set P(S) of the set S = { Φ, { 1,2, 3 } , 3 , {{1,2}} } is?

Convert the following sentences into symbolic form. i) All planets revolves around sun in an elliptical orbit ii) No student who is intelligent will fail.

In how many different ways can 3 elements be selected in order from a set with five 10 when repetition is allowed?

Write the following into symbolic form:

Some student in this class has studied programming.

Symbolic Logic

Can you figure out the values of the following below? Why or why not

1.    (H ≡≡ A) ⊃J (G ≡≡ B)

2.    ~ (X· G)

For each of the following pairs of sentences below, indicate whether (1) is a sufficient condi[1]tion for (2), a necessary condition for (2), both, or neither

3.   (I) Amy is not a student. (2) Amy is neither a student nor a teacher.

4.   (1) John loves Mary. (2) Someone loves Mary.

Symbolic Logic

Compute the truth values of the following, given that A, B, and C are true, and X, Y, and Z are false.

1.   ~ [((A⊃J ~B) ⊃J~C) ⊃J~X]

2.  [(((A⊃J B) ⊃J X) ⊃J Z) ⊃J Y] ⊃J [((X ⊃J Z) ⊃J A) ⊃J X]

Compute the truth values of the following, using the values given in the above Exercise, but without being given the values of G, H, or f.

3. (A∨B) ≡((G∨H) ⊃A)

4.    (G ≡≡ (H· A)) ⊃J «~H V I) ⊃J (X⊃J Z))

How many ways are there to select 15 countries in the United Nations to serve on a council if 4 are selected from a block of 35, 5 are selected from a block of 40, and the others are selected from the remaining 55 countries?

Show that (p → q) ∧ (p → r) and p → (q ∧ r) are logically equivalent using

logical equivalence laws.

Draw a Venn diagram to represent each of the following:

(a) AUB

(b) (AUB)

(c) An (BUC)

(d) (ANB) UC

(e) AnBnC