R is not symmetric as (b,c) does not imply (c,b) is in R. It is reflexive and transitive.

R is neither reflexive, symmetric, nor transitive.

Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (15 * 5) / 10 = 7.5Ω.

For balance, R1/R2 = R3/R4, thus R4 = (R2 * R3) / R1 = (20 * 30) / 10 = 60Ω.

The bridge is not balanced because 10/20 ≠ 30/60.

Using the balance condition R1/R2 = R3/R4, we have 2/3 = 6/R4. Solving gives R4 = 4Ω.

Using the balance condition R1/R2 = R3/R4, we have 2/3 = 6/R4. Solving gives R4 = 4Ω.

Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (10 * 15) / 5 = 30Ω.

For balance, R4 must be 30Ω since 5/15 = 10/30.

S is the sister of U as they share the same parents, T.

T is the son of V, making V the grandfather of S.

S is the sister of T, and U is the brother of T, so S is also the sister of U.

Since sec A = 1/cos A, we have cos A = 1/2.

Since sec θ = 1/cos θ, if sec θ = 2, then cos θ = 1/2.

sec(x) = 1/cos(x), so cos(x) = 1/2.

The intersection of sets A and B includes only the elements that are present in both sets, which are {b, c}.

The intersection A ∩ B includes elements that are both even and prime, which is {2}.

The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 15 + 10 - 5 = 20.

The intersection of sets A and B is the set of elements that are common to both sets. Therefore, the intersection is {3, 4}.

The intersection of sets A and B is the set of elements that are common to both sets, which is {4, 5}.

Hybrid sets can include elements that are exclusive to either of the original sets, making them versatile in composition.

Both 12 and 9 are multiples of 3 and less than 15, but 12 is the first option listed.

The integer 10 is not divisible by 3, hence it is not a member of set C.

Hybrid sets can include additional elements beyond those found in the original sets, allowing for greater flexibility.

The range of values for set D is from 2 to 8, inclusive.

The difference P - Q includes elements in P that are not in Q, which is {1, 2}.

The intersection of sets P and Q includes elements that are both even and prime. The only even prime number is 2.

The symmetric difference of sets R and S includes elements that are in either set but not in both. Thus, it is {1, 2, 3, 6, 7}.

The difference T - U includes elements that are in set T but not in set U, which is {1}.

The union of sets X and Y includes all unique elements from both sets. Thus, the union is {a, b, c, d}.