2. If x is a parent of y, then x is older than y. If x is mother of y, then x is parent of y. Lulu is mother of Fifi. Therefore, Lulu is older than Fifi 4. Take a look at the below graph, we will use the Breadth-First Search algorithm to traverse through …
Assignment must be submitted by 28th July, 2024
We studied propositional logic. Lets take a statement “x > 5” is this statement a proposition? The answer is no. Whenever the statements have variable(s) in them we cannot say those statements as a proposition. The question here is can we make such statements to propositions? The answer here is yes. In the above statement …
If two propositions are semantically identical then we say those two propositions are “equivalent”. If two propositions P(p,q,r,.…) and Q(p,q,r,….) where p,q,r,… are propositional variables have the same truth values in every possible case, the propositions are called logically equivalent and denoted as, P(p,q,r,.…) ≡ Q(p,q,r,….) To test whether two propositions P and Q are …
A compound proposition that is always true, no matter what the truth values of the atomic propositions that contain in it, is called a tautology. For e.g. p ∨ ¬p is always true. A compound proposition that is always false is called contradiction. For e.g. p ∧ ¬p is always false. A compound …
Logical operators are used to construct mathematical statements having one or more propositions by combining the propositions. The combined proposition is called compound Proposition. The truth table is used to get the relationship between truth values of propositions. Here we present the logical operators along with their behavior in truth table: 1. Negation (NOT): Examples: …
Logic: Logic is a language for reasoning. Logic is a formal study of mathematics; it is the study of mathematic reasoning and proofs itself. Since logic can helps us to reason the mathematical models it needs some rules associated with logic so that we can apply those rules for mathematical reasoning. It helps us to …
Discrete Mathematics deals with discrete objects that can be counted and are not connected for e.g. houses, trees, desks, integers, etc. Discrete mathematics is the study of mathematical structures that are countable or otherwise distinct and separable. Examples of structures that are discrete are combinations, graphs, and logical statements. It isn’t a branch of mathematics. It is …
Prove that the inverse and converse of conditional statements are logically equivalent. Show that conditional statement is logically equivalent to its contrapositive. Define tautology, contradiction and contingency with example. Construct the truth table for the proposition Find the negation of the following: All students study for exams. Some politicians are honest and sincere. Every McDonald’s …
Assume the truth values of the following statements:“Bleebs are quills” is TRUE“Blarbs are snarfs” is FALSE“Blairs are mares” is TRUEDetermine whether the following statements are TRUE or FALSE: Bleebs are quills or Blairs are mares. If Blairs are mares then Blarbs are snarfs. If Blarbs are snarfs then Blairs are mares. If Bleebs are not …
