Search & Filtering
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
Let A = {x € N: 3 ≤ x ≤ 13}, B = {x € N : x is even}, and C = {x EN: x is odd}.
(a) Find An B.
(b) Find A UB.
(c) Find Bn C..
(d) Find BUC.
Write the statements in symbolic form
, and
and the indicated letters to
represent compound statements.
a) Let s = “stocks are increasing” and i = ”interest rates are steady”.
i. Stocks are increasing but interest rates are steady.
ii. Neither are stocks increasing nor are interest rates steady
A group of students study at least one of the following subjects:biology, chemistry and physics. 36 of them study chemistry, 39 study biology and 41 study physics.15 study physics. 9 study all the three subjects. @draw a Venn diagram to illustrate this information.(b)from your diagram find:(1) the total number of students in the group.(2)the number of students who study only one subject.@the universal set U={2,3,5,7},p={2,5}and Q={5,7}find:(1)(PnQ),(2)P'UQ'. State the relationship between (1)and(2)(b)in a class of 50 students, 30 offer economics,17 offer government and 7 offer neither economics nor government. How many students offer both subjects.
