Economics Q1. Please Explain if the following claims are true or false: (In the relationship between NE, subgame perfect equilibria, backward induction, perfect bayesian equilibrium, and sequential equilibrium): 1- Backward induction solution is a Nash equilibrium solution and not every NE is a backward induction. 2- Not all Nash equilibria are sequentially rational. 3- All Backward induction solutions are sequentially rational. 4- SPNE solutions are Nash equilibria. 5- SPNE solutions are sequentially rational if the game has at least one proper subgame. If it only has improper subgame then it may not be sequentially rational. 6- PBE solutions are Nash equilibrium and SPNE. 7- PBE solutions are sequentially rational no matter what. 8- Every sequential equilibrium is a NE. 9- Every subgame optimal equilibrium is a NE