equality.php

<?php

const ✓ = true;
const ✕ = false;

function ≠($left, $right) {
    return $left != $right;
}

function ≅($left, $right) {
    return ($left > $right - 0.0001) && ($left < $right + 0.0001);
}

function ≡($left, $right) {
    return $left === $right;
}

function ≢($left, $right) {
    return $left !== $right;
}

set.php

<?php

function ∅() {
    return array();
}

function ∃($value, array $set) {
    return ✕ !== array_search($value, $set, true);
}

function ∄($value, array $set) {
    return ✕ === array_search($value, $set, true);
}

function ∩(array $set1, array $set2) {
    return array_intersect($set1, $set2);
}

function ∪(array $set1, array $set2) {
    return array_merge($set1, $set2);
}

function ⊂(array $subset, array $superset) {
    return $subset == ∩($subset, $superset);
}

function ⊃(array $superset, array $subset) {
    return ⊂($subset, $superset);
}

function ⊄(array $subset, array $superset) {
    return !⊂($subset, $superset);
}

function ⊅(array $superset, array $subset) {
    return !⊂($subset, $superset);
}