Problem

a. Can the sets $\{1,2,3,4,5\}$ and $\{m, n, o, b, t\}$ be placed in a one-to-one correspondence? No Yes b. Can the sets $\{b, t, 1, m\}$ and $\{b, t, w\}$ be placed in a one-to-one correspondence? No Yes c. Can the sets $\{a, b, c, \ldots, f\}$ and $\{2,4,6, \ldots, 10\}$ be placed in a one-to-one correspondence? No Yes d. Can the sets $\{\mathrm{t} \mid \mathrm{t}$ is a letter in the word can $\}$ and $\{1,2,3,4\}$ be placed in a one-to-one correspondence? Yes No e. Can the sets $\{\square, \nabla\}$ and $\{b, t\}$ be placed in a one-to-one correspondence? No Yes

Solution

Step 1 :\(\text{a. Since both sets have 5 elements, they can be placed in a one-to-one correspondence.}\)

Step 2 :\(\text{b. The first set has 4 elements and the second set has 3 elements, so they cannot be placed in a one-to-one correspondence.}\)

Step 3 :\(\text{c. Both sets have 6 elements, so they can be placed in a one-to-one correspondence.}\)

Step 4 :\(\text{d. The first set has 3 unique elements (c, a, n) and the second set has 4 elements, so they cannot be placed in a one-to-one correspondence.}\)

Step 5 :\(\text{e. Both sets have 2 elements, so they can be placed in a one-to-one correspondence.}\)

Step 6 :\(\boxed{\text{Final Answer:}}\)

Step 7 :\(\boxed{\text{a. Yes}}\)

Step 8 :\(\boxed{\text{b. No}}\)

Step 9 :\(\boxed{\text{c. Yes}}\)

Step 10 :\(\boxed{\text{d. No}}\)

Step 11 :\(\boxed{\text{e. Yes}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/26468/

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