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Show ((p ∨ q) ∧ ¬(¬p ∧ (¬q ∨ ¬r))) ∨ (¬p ∧ ¬q) ∨ (¬p ∧ ¬r) is tautology, by using replacement process.
How many license plates can be made using either two or three letters followed by either two or three digits?
The argument is p→~q,~r→p,q|–r in true table in mathematical foundations of computer science
A school organized a book fair and in this book fair a book seller is selling his books under the following rules:
There are three different packages available.
First package contains 2 Islamic books, 2 Science books and 2 Geography books, second package contains 2 Islamic books, 4 Science books and 1 Geography books and third package contains 3 Islamic books, 4 Science books and 5 Geography books. The book fair has a total of 250 Islamic books, 300 Science books, and 270 Geography books. First package makes a profit of Rs. 120, second package makes Rs.100 and third package makes Rs.270 per pack.
How many packs should be made to maximize book fair profits?
What will the profit be?
Define and give examples of injective surjective and bijective functions. Check the injectivity and surjectivity of the following function f: NN given by f(x)=x2
Obtain the Conjunctive Normal Form of (x^y) V (-x^y)
Show that the following logical equivalences hold for the
Peirce arrow ↓, where P ↓ Q ≡ ∼(P ∨ Q).
a. ∼P ≡ P ↓ P
b. P ∨ Q ≡ (P ↓ Q) ↓ (P ↓ Q)
c. P ∧ Q ≡ (P ↓ P) ↓ (Q ↓ Q)
H d. Write P → Q using Peirce arrows only.
e. Write P ↔ Q using Peirce arrows only.
There are 10 stalls for animals in an exhibition. Three animals; lion, pussycat
and horse are to be exhibited. Animals of each kind are not less than 10 in
number. What is the possible number of ways of arranging the exhibition?
Consider a Boolean expression Ex,y,z=(x^-z)v(y^z). Find disjunctive and conjunctive normal form.
- Consider a Boolean expression Ex,y,z=xzv(y^z). Find disjunctive and conjunctive normal form.
