(Solved): ans only 1. For any propositions \( p \) and \( q \), we have \( p \vee(q \vee \neg q)=T \). 2. The ...

1. For any propositions \( p \) and \( q \), we have \( p \vee(q \vee \neg q)=T \). 2. The statement \( \forall x \in \mathbb{R} \exists y \in \mathbb{R}(x y=1) \) is false. 3. If \( A=\{\phi,\{\phi\}\} \), then \( |\mathcal{P}(A)|=2 \). 4. If the function \( f: A \rightarrow B \) is not \( 1-1 \), then \( \exists x, y \in A \) such that \( f(x)=f(y) \). 5. A mapping \( f: A \rightarrow B \) is called a function if and only if for all \( a \in A \), there is an element \( b \in B \) such that \( f(a)=b \). 6. In any directed graph \( G=(V, E) \), we have \( \sum_{v \in V} \) in-deg \( (v)+\sum_{v \in V} \operatorname{out-deg}(v)=2|E| \). 7. The cube graph \( Q_{4} \) has 16 vertices and 32 edges. 8. The cube graph \( Q_{3} \) is not planar. 9. There are 18 edges in the complete bipartite graph \( K_{9,2} \). 10. It is possible to draw an undirected graph with 33 edges and 4 vertices where the degrees are \( 22,33,6,5 \). respectively.