Definining \$$(true \multimap false) = false\$$ and \$$(true \multimap true) = (false \multimap true) = (false \multimap false) = true\$$ should work.

1. the falsity of \$$(true \wedge true) \leq false\$$ requires the falsity of \$$true \leq (true \multimap false)\$$, hence the falsity of \$$(true \multimap false)\$$.
2. the truth of \$$(true \wedge true) \leq true\$$ requires the truth of \$$true \leq (true \multimap true)\$$, hence the truth of \$$(true \multimap true)\$$.
3. the truth of \$$(true \wedge false) \leq x\$$ for all \$$x \in \mathbb{B}\$$ requires the truth of \$$true \leq (false \multimap x)\$$, hence the truth of \$$(false \multimap x)\$$ for all \$$x \in \mathbb{B}\$$.
4. the truth of all expressions of the form \$$(false \wedge x) \leq y\$$ and \$$false \leq z\$$ for any x,y,z in \$$\mathbb{B}\$$ implies that they give no further restrictions on \$$\multimap\$$.