Engineering Maths-I Quiz

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)}

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.

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.

<p>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}</p> Signup and view all the answers

<p>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)</p> Signup and view all the answers