Consider the following expression grammar. The seman­tic rules for expression calculation are stated next to each grammar production.

$$\eqalign{ & E \to number\,\,\,\,\,E.val = number.val \cr & \,\,\,\,\,\,\,\,\,\,\,|E\,\,' + '\,\,E\,\,\,\,\,\,{E^{\left( 1 \right)}}.val = {E^{\left( 2 \right)}}.val + {E^{\left( 3 \right)}}.val \cr & \,\,\,\,\,\,\,\,\,\,\,|\,E\,\,' \times '\,\,E\,\,\,\,\,\,\,{E^{\left( 1 \right)}}.val = {E^{\left( 2 \right)}}.val \times {E^{\left( 3 \right)}}.val \cr} $$

Assume the conflicts in the previous question are resolved and an LALR(1) parser is generated for parsing arithmetic expressions as per the given grammar. Consider an expression
3 × 2 + 1.
What precedence and associativity properties does the generated parser realize?

Consider the following expression grammar. The seman­tic rules for expression calculation are stated next to each grammar production.

$$\eqalign{ & E \to number\,\,\,\,\,E.val = number.val \cr & \,\,\,\,\,\,\,\,\,\,\,|E\,\,' + '\,\,E\,\,\,\,\,\,{E^{\left( 1 \right)}}.val = {E^{\left( 2 \right)}}.val + {E^{\left( 3 \right)}}.val \cr & \,\,\,\,\,\,\,\,\,\,\,|\,E\,\,' \times '\,\,E\,\,\,\,\,\,\,{E^{\left( 1 \right)}}.val = {E^{\left( 2 \right)}}.val \times {E^{\left( 3 \right)}}.val \cr} $$

The above grammar and the semantic rules are fed to a yacc tool (which is an LALR (1) parser generator) for parsing and evaluating arithmetic expressions. Which one of the following is true about the action of yacc for the given grammar?

Consider the grammar

$$S \to \left( S \right)\,|\,a$$

Let the number of states in SLR(1), LR(1) and LALR(1) parsers for the grammar be n₁, n₂ and n₃ respectively.

The following relationship holds good

Consider the grammar

$$E \to E + n\,|\,E \times n\,|\,n$$

For a sentence n + n × n, the handles in the right-sentential form of the reduction are