5 Questions
Find the products of sets A and (B∩C), A and (B∪C), (A×B)∪(A×C), and (A×B)∩(A×C)
i. $A×(B∩C) = {3}$ ii. $A×(B∪C) = {1, 2, 3, 4, 5, 6}$ iii. $(A×B)∪(A×C) = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}$ iv. $(A×B)∩(A×C) = {(1, 3), (2, 3), (3, 3)}
Show the logical equivalence between p˅(q˄r) and (p˅q)˄(p˅r)
To show the logical equivalence between $p˅(q˄r)$ and $(p˅q)˄(p˅r)$, we can use the distributive law of logic. By applying the distributive law, we can demonstrate that the two expressions are equivalent.
Determine if (p→q)→r and (p→q)˄(q→r) are logically equivalent
The expressions (p→q)→r and (p→q)˄(q→r) are not logically equivalent. One way to show this is by constructing a truth table to compare the truth values of the two expressions for all possible combinations of truth values for p, q, and r.
Find the union, intersection, set difference (A−B), set difference (B−A), and symmetric difference (AΔB) of sets A and B using a Venn diagram
Union: $A∪B = {a, b, c, d, e, f, g, h}$, Intersection: $A∩B = {a, b, c, d, e}$, Set difference (A−B): $A−B = {}$, Set difference (B−A): $B−A = {f, g, h}$, Symmetric difference (AΔB): $AΔB = {f, g, h}
Determine the percentage of Kashmiris who like both apples and oranges based on the survey results
To determine the percentage of Kashmiris who like both apples and oranges, we can use the principle of inclusion-exclusion. The percentage of Kashmiris who like both apples and oranges can be found using the formula: Percentage of (A∩B) = Percentage of A + Percentage of B - Percentage of (A∪B)
Test your understanding of Engineering Maths-I with this quiz covering topics such as functions, direct proofs, and logical equivalences. Practice solving mathematical problems and proving statements to strengthen your knowledge in this subject.
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