In june of year 1, edgar's wife cathy died and edgar did not remarry during the year. what is his filing status for year 1 (assuming they did not have any dependents) ?

His status for the year would be married filing jointly

Because of the tax system in the United States, if he doesn't remarry then the deceased would legally still be considered as if alive and married when calculating taxes for the year. If he remarries then another way of calculating paid taxes would happen.