The Ramsey number $R(G)$ of a graph $G$ is the smallest $n$ such that in any red/blue colouring of the edges of $K_{n}$ there is a monochromatic copy of $G$.

Show that $R\left(K_{t}\right) \leqslant\left(\begin{array}{c}2 t-2 \\ t-1\end{array}\right)$ for every $t \geqslant 3$.

Let $H$ be the graph on four vertices obtained by adding an edge to a triangle. Show that $R(H)=7$.