Let A, B, C and D be four non-empty sets. The | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The contrapositive of a conditional statement $p \rightarrow q$ is $\sim q \rightarrow \sim p$.Given the statement: "If $A \subseteq B$ and $B \su

Vedclass · Accepted Answer

If $A 
ot\subseteq C,$ then $A 
ot\subseteq B$ or $B 
ot\subseteq D$

Vedclass · Answer

(A) The contrapositive of a conditional statement $p ightarrow q$ is $\sim q ightarrow \sim p$.Given the statement: "If $A \subseteq B$ and $B \subseteq D,$ then $A \subseteq C$."Let $p$ be $(A \subseteq B) \land (B \subseteq D)$ and $q$ be $(A \subseteq C)$.The negation $\sim q$ is $A 
ot\subseteq C$.The negation $\sim p$ is $\sim((A \subseteq B) \land (B \subseteq D))$,which by De Morgan's Law is $(A 
ot\subseteq B) \lor (B 
ot\subseteq D)$.Thus,the contrapositive is: "If $A 
ot\subseteq C,$ then $A 
ot\subseteq B$ or $B 
ot\subseteq D$."

Let $A, B, C$ and $D$ be four non-empty sets. The contrapositive statement of "If $A \subseteq B$ and $B \subseteq D,$ then $A \subseteq C$" is

Similar Questions

Given the following two statements:
$(S_{1}): (q \vee p) \rightarrow (p \leftrightarrow \sim q)$ is a tautology.
$(S_{2}): \sim q \wedge (\sim p \leftrightarrow q)$ is a fallacy.
Then:

The negation of the statement $''96$ is divisible by $2$ and $3''$ is

Consider the following statements:
Statement $I$: If a quadrilateral $ABCD$ is a square,then all of its sides are equal.
Statement $II$: If all the sides of a quadrilateral $ABCD$ are equal,then $ABCD$ is a square.
Then:

By giving a counterexample,show that the following statement is false: "If $n$ is an odd integer,then $n$ is prime."

The statement pattern $(p \lor q) \to \sim r$ is logically equivalent to

Vedclass Test Series

Exam Paper Generator

Online Exam Module