Advertisements
Advertisements
प्रश्न
Using the Venn diagram, examine the logical equivalence of the following statements:
(a) Some politicians are actors.
(b) There are politicians who are actors.
(c) There are politicians who are not actors.
Advertisements
उत्तर
Let the universal set be U.
U : The set of all human beings.
Let P: The set of all politicians.
A: The set of all actors.
Now, the Venn diagrams for statements (a). (b) and (c) are as follows:
(a)
(b)
(c)
By Venn diagrams, we observe that the truth set of statements (a) and (b) are equal. Hence statements (a) and (b) are logically equivalent.
APPEARS IN
संबंधित प्रश्न
Draw appropriate Venn diagram for the following:
(A ∪ B)'
Draw appropriate Venn diagram for the following:
A' ∩ B'
In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.
Draw a Venn diagram for the truth of the following statement :
All rational number are real numbers.
If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find:
\[\left( A \cap B \right) \cap \left( B \cap C \right)\]
Let \[A = \left\{ x: x \in N \right\}, B = \left\{ x: x - 2n, n \in N \right\}, C = \left\{ x: x = 2n - 1, n \in N \right\}\] and D = {x : x is a prime natural number}. Find: \[B \cap C\]
Let A = {3, 6, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20}. Find: \[C - A\]
Let A = {3, 6, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20}.
Find: \[B - C\]
Let A = {3, 6, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20}.
Find: \[B - D\]
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that \[\left( A \cup B \right)' = A' \cap B'\]
From the given diagram find :
A ∪ B
Use the given Venn-diagram to find :
B'
Two sets A and B are such that A ∩ B = Φ. Draw a venn-diagram to show the relationship between A and B. Shade the region representing :
A ∪ B
State the sets representing by the shaded portion of following venn-diagram :
From the given diagram, find :
(i) (A ∪ B) - C
(ii) B - (A ∩ C)
(iii) (B ∩ C) ∪ A
Verify :
A - (B ∩ C) = (A - B) ∪ (A - C)
Using the given diagram, express the following sets in the terms of A and B. {a, d}
Using the given diagram, express the following sets in the terms of A and B. {a, d, c, f, g, h}
Draw a Venn diagram for the truth of the following statement.
Some share brokers are chartered accountants.
Draw the Venn diagrams to illustrate the following relationship among sets E, M and U, where E is the set of students studying English in a school, M is the set of students studying Mathematics in the same school, U is the set of all students in that school.
All the students who study Mathematics study English, but some students who study English do not study Mathematics.
Take the set of natural numbers from 1 to 20 as universal set and show set X using Venn diagram.
X = {x | x ∈ N, and 7 < x < 15}
