Symbol Values
1. Let's start by calculating each symbol value step-by-step.
2. For $$\Omega$$:
$$\Omega = 28 - \frac{2}{6} = 28 - \frac{1}{3} = \frac{84}{3} - \frac{1}{3} = \frac{83}{3}$$
3. For $$\varepsilon$$, the formula given is $$5 + \frac{4}{5} x$$ but no value for $$x$$ is provided, so we move to another expression with $$\varepsilon$$ later.
4. For $$\Delta$$:
$$\Delta = -32 + 1 = -31$$
5. For $$\bigcirc$$ (◎):
$$\bigcirc = 14 - \left( \frac{3}{5} + \frac{11}{6} - \frac{2}{5} \right)$$
Calculate inside the bracket first:
$$ \frac{3}{5} - \frac{2}{5} = \frac{1}{5}$$
So inside the bracket:
$$ \frac{1}{5} + \frac{11}{6} = \frac{6}{30} + \frac{55}{30} = \frac{61}{30}$$
Therefore:
$$ \bigcirc = 14 - \frac{61}{30} = \frac{420}{30} - \frac{61}{30} = \frac{359}{30}$$
6. For $$\triangledown$$ (▼):
$$ \triangledown = -1 \times \bigcirc + 2 = -1 \times \frac{359}{30} + 2 = - \frac{359}{30} + \frac{60}{30} = -\frac{299}{30}$$
7. For $$\varepsilon$$ again:
Given two expressions:
$$ \varepsilon = 5 + \frac{4}{5} x $$ (unsolved without $$x$$)
and
$$ \varepsilon = 16 - (4 - 8) - 18 + (-2) $$
Calculate the second expression:
$$ 4 - 8 = -4$$
So:
$$ 16 - (-4) - 18 + (-2) = 16 + 4 - 18 - 2 = 0$$
Therefore, $$\varepsilon = 0$$ from the second expression.
8. For $$\bullet$$ (•):
$$ \bullet = -6 \times \frac{3}{4} + \left(-\frac{1}{2}\right) = -\frac{18}{4} - \frac{1}{2} = -\frac{9}{2} - \frac{1}{2} = -5$$
9. For $$\varepsilon$$ again, given:
$$ \varepsilon = -1 - \blacksquare$$
We know $$\varepsilon = 0$$ from step 7, so:
$$ 0 = -1 - \blacksquare \implies \blacksquare = -1$$
10. For $$\blacksquare$$ (■):
Given:
$$ \blacksquare = (\bigcirc - \triangledown) + 2 $$
Calculate:
$$ \bigcirc - \triangledown = \frac{359}{30} - \left(-\frac{299}{30}\right) = \frac{359}{30} + \frac{299}{30} = \frac{658}{30} = \frac{329}{15}$$
Add 2:
$$ \blacksquare = \frac{329}{15} + 2 = \frac{329}{15} + \frac{30}{15} = \frac{359}{15}$$
But earlier we found $$\blacksquare = -1$$ indicating contradictory equations or different instances; the problem likely requires choosing the value from the previous equation (step 9).
11. Summary results:
$$\Omega = \frac{83}{3}$$
$$\Delta = -31$$
$$\bigcirc = \frac{359}{30}$$
$$\triangledown = -\frac{299}{30}$$
$$\varepsilon = 0$$
$$\bullet = -5$$
$$\blacksquare = -1$$
12. The tables provided list values with Arabic headers; they are data sets for verification but no operations requested.
Final answers are as above.