1. (11 points) Consider the classic Connect Four game, where players choose a color and then take turns dropping colored tokens into a six-row, seven-column vertically suspended grid. The objective of the game is to be the first to form a horizontal, vertical, or diagonal line of four of one's own tokens. Suppose that two players, one with yellow and the other with red tokens, are playing the game. Propositional functions $Y(i,j)$, $R(i,j)$, and $B(i,j)$ assert that the square in the $i$-th row and the $j$-th column (refer to the figure) contains a yellow, a red, and no token, respectively. Please use these predicates together with the connectives permitted to translate the statements in (a) to (c) into logic expressions. Permitted connectives are $\lor, \land, \neg, \rightarrow$, and the pair of parentheses "()". For any propositional function $f(x,y)$, you should use the notation $\bigvee_{i=m}^{n} f(i,j)$ for $f(m,j) \lor f(m+1,j) \lor \cdots \lor f(n,j)$ and the notation $\bigwedge_{i=m}^{n} f(i,j)$ for $f(m,j) \land f(m+1,j) \land \cdots \land f(n,j)$.

(a) (4 points) Four squares in the 2nd row contains four red tokens in a row.

(b) (4 points) Each column contains at least a yellow token.

(c) (3 points) If the square in the $i$-th row and the $j$-th column contains a token, the square contains either a red or a yellow token but not both.